Estimating the Cross Immunity Between Drifted Strains of Influenza A/H3N2
Junling Ma
Abstract: To determine the cross-immunity between influenza strains, we design a novel statistical method, which uses a theoretical model and clinical data on attack rates and vaccine efficacy among school children for two seasons after the 1968 A/H3N2 influenza pandemic. This model incorporates the distribution of susceptibility and the dependence of cross-immunity on the antigenic distance of drifted strains. We find that the cross-immunity between an influenza strain and the mutant that causes the next epidemic is 88%. Our method also gives estimates of the vaccine protection against the vaccinating strain, and the basic reproduction number of the 1968 pandemic influenza.

A game-theoretic model for emergency preparedness among NGO's
Myles Nahirniak
Natural disasters in the United States last year resulted in a cost of almost \$100 billion. In this talk, we consider the issue of disaster relief efforts by Non-Governmental Organizations (NGOs). We develop an asymmetric game to describe the behavior of two NGOs competing to purchase supplies. The players' payoff matrices depend on their level of preparedness for a disaster, and failure to make adequate provisions results in financial penalty. A replicator dynamics is introduced to investigate the time evolution of the players' optimal strategies, as well as stability. Finally, we impose a shared constraint, in order to place an upper limit on the total available supplies, and examine the effect on the players' strategies.

Distribution Electricity Pricing under Uncertainty
Yury Dvorkin
Distribution locational marginal prices (DLMPs) facilitate the efficient operation of low-voltage electric power distribution systems. We propose an approach to internalize the stochasticity of renewable distributed energy resources (DERs) and risk tolerance of the distribution system operator in DLMP computations. This is achieved by means of applying conic duality to a chance-constrained AC optimal power flow. We show that the resulting DLMPs consist of the terms that allow to itemize the prices for the active and reactive power production, balancing regulation, and voltage support provided. Finally, we prove the proposed DLMP constitute a competitive equilibrium, which can be leveraged for designing a distribution electricity market, and show that imposing chance constraints on voltage limits distort the equilibrium.

An Empirical Quantification of the Impact of Choice Constraints on Generalizations of the 0-1 Knapsack Problem using CPLEX®
Yun, Lu Francis, Vasko
It has been well-known for some time that adding choice constraints to certain types of knapsack formulations improves the solution time for these problems when using integer programming solvers, but by how much? In this paper, by using the integer programming option of CPLEX, we provide comprehensive empirical and analytical evidence of the impact of choice constraints on two important categories of knapsack problems. Specifically, we show using multidimensional knapsack problems (MKP) and multi-demand multidimensional knapsack problems from Beasley’s OR-Library that adding choice constraints reduces solution time by more than 99.9%. Additionally, using these same problem instances, we show that even if only some of the variables have choice constraints imposed on them, the CPLEX solution times are drastically reduced. These results provide motivation for operations research practitioners to check if choice constraints are applicable when solving real-world problems involving generalizations of the 0-1 knapsack problem.

Novel compartmental models of infectious disease
Scott Greenhalgh
Many methodologies in disease modeling have proven invaluable in the evaluation of health interventions. Of these methodologies, one of most fundamental is compartmental modeling. Compartmental models come in many different forms with one of the most general characterizations occurring from the description of disease dynamics with nonlinear Volterra integral equations. Despite this generality, the vast majority of disease modellers prefer the special case whereby the nonlinear Volterra integral equations are reduce to systems of differential equations through the traditional assumptions that 1) the infectiousness of a disease corresponds to incidence, and 2) the duration of infection follows either an Exponential distribution or an Erlang distribution. However, these assumptions are not the only ones that simplify nonlinear Volterra integral equations in such a way. In this talk, we demonstrate how a biologically more accurate description of the infectiousness of a disease combines with nonlinear Volterra integral equations to yield a novel class of differential equation compartmental models, and then illustrate the novelty of this approach with several examples.

Generalized Nash games and replicator dynamics
Monica Cojocaru
In this talk I plan to introduce an evolutionary generalized Nash game (eGN). Generalized Nash games were introduced in the 50’s, and represent models of noncooperative behaviour among players whose both strategy sets and payoff functions depend on strategy choices of other players. Among these games, a specific class is represented by evolutionary games, which consist of populations where individuals play many times, against many different opponents, with each contributing a relatively small contribution to the total reward. Given strategies {1, ..., n}, an individual of type i is one using strategy i, where xi is the frequency of type i individuals in the population. Thus the vector x = (x1, ..., xn) in the unit simplex is the state of the population. Interaction between players of different types can be described by linear or nonlinear payoffs. One known dynamic evolution of such a game is described by a replicator dynamics. However, assuming constraints imposed on the strategy sets of players (upper limits on resources for instance) the classic replicator dynamics is not appropriate anymore. In these cases we show that we can reinterpret the game dynamics of an eGN differently. The new dynamics and its relation to evolutionary steady states is investigated.

Distributionally Robust Chance Constrained Optimal Power Flow Assuming Unimodal Distributions with Misspecified Modes
Bowen Li
Chance-constrained optimal power flow (CC-OPF) formulations have been proposed to minimize operational costs while controlling the risk arising from uncertainties like renewable generation and load consumption. To solve CC-OPF, we often need access to the (true) joint probability distribution of all uncertainties, which is rarely known in practice. A solution based on a biased estimate of the distribution can result in poor reliability. To overcome this challenge, recent work has explored distributionally robust chance constraints, in which the chance constraints are satisfied over a family of distributions called the ambiguity set. Commonly, ambiguity sets are only based on moment information (e.g., mean and covariance) of the random variables; however, specifying additional characteristics of the random variables reduces conservatism and cost. Here, we consider ambiguity sets that additionally incorporate unimodality information. In practice, it is difficult to estimate the mode location from the data and so we allow it to be potentially misspecified. We formulate the problem and derive a separation-based algorithm to efficiently solve it. Finally, we evaluate the performance of the proposed approach on a modified IEEE-30 bus network with wind uncertainty and compare with other distributionally robust approaches. We find that a misspecified mode significantly affects the reliability of the solution and the proposed model demonstrates a good trade-off between cost and reliability.

OPTIMIZATION PROBLEMS IN SPACE ENGINEERING
giorgio fasano
Space engineering has since the very beginning represented a field where optimization methodologies were inevitable. In the earliest studies, the primary concern was related to the viability of the mission to accomplish. Therefore optimization generally focused on mission analysis aspects, with specific attention to technical feasibility and mission safety. Space engineering projects typically required the analysis and optimization of trajectories and fuel consumption. As time has passed a number of further issues, related, inter alias, to logistics and systems engineering aspects, have become increasingly important. Among the various optimization challenges relevant to this context, object packing, in the presence of balancing conditions, as well as additional requirements, are of great relevance. This wide class of problems are notorious for being NP-hard. Some packing scenarios arising in space applications are illustrated, pointing out the specificity of the instances to cope with. An overall global optimization heuristic approach is outlined, introducing a tailored modeling philosophy, as opposed to a purely algorithmic one. The orthogonal packing of three-dimensional “tetris-like” items, within a convex polyhedral domain, is briefly discussed. Additional constraints are also investigated, including balancing requirements. The general spacecraft control dispatch problem is proposed as a further optimization challenge in space applications. A dedicated controller has the task of determining the overall control action, to achieve the desired system attitude. A number of thrusters are available to exert the overall forces and torques, as required. Their positions and orientations on the external surface of the spacecraft is usually critical, since different layouts may yield different performance, in terms of energy usage throughout the entire mission. Once on orbit, the requested spacecraft control has to be dispatched, in compliance with given operational constraints, through the thrusters, with the aim of minimizing the overall propellant consumption. The relevant mathematical models and the overall heuristic approach adopted are overviewed.

Using a realistic SEIR model to assess the burden of vaccine-preventable diseases in China and design optimal mitigation strategies
John Glasser
Mathematical modelers often make simplifying assumptions, but only rarely ascertain the consequences. We developed an age-stratified population model with births, deaths, aging and – because non-random mixing exacerbates the effect of heterogeneity on reproduction numbers (JTB 2015; 386:177-87) – realistic mixing between age groups. Using this model, we assessed the burden of congenital rubella syndrome (CRS) and evaluated the impact of demographic details on optimal vaccination strategies for disease elimination. Our estimate of the burden of CRS is 5 times that of Vynnycky, et al. (PLoS ONE 2016; 11(3): e0149160), and the 2014 serological profile suggests that it will dramatically increase absent timely immunization of susceptible adolescents. As is typical of developed countries, China’s mortality schedule is type I. The impact on the optimal strategy of assuming type II mortality is modest, but our approach will be useful when and wherever vaccine availability is limited.

On Decomposition Methods for Generalized Nash Equilibrium Problems
Tangi Migot
Generalized Nash equilibrium problems (GNEP) are a potent modeling tool that have developed a lot in recent decades. Much of this development has centered around applying variational methods to the so-called GNSC, a subset of GNEP where each player has the same constraint set. One popular approach to solve the GNSC is to use the apparent separability of each player to build a decomposition method. This method has the benefit to be easily implementable and can be parallelized. Our aim in this talk is to show an extension of the decomposition methods to the GNEP, that is not necessarily with shared constraints.

Risk-Sensitive Economic Dispatch: Theory and Algorithms
Subhonmesh Bose
In economic dispatch problems with uncertain supply or network conditions, an inherent tradeoff arises between power procurement costs and reliability of power delivery. In this talk, we explore risk-sensitive economic dispatch problem formulations, where risk is modeled via the conditional value at risk (CVaR) measure. Such formulations allow a system operator to explore the cost-reliability tradeoff. We provide customized algorithms to solve these risk-sensitive problems—a critical region exploration algorithm to guard against possible line failures and an online stochastic primal-dual subgradient method to dispatch against uncertain wind.

A General Lagrange Multipliers Based Approach for Object Packing Applications
Janos D. Pinter
We have extended our previous work on packing circles, ellipses and generalized ellipses (ovals) in regular convex polygons. Now we can pack ellipses, ovals and smooth polygons into convex and non-convex regions formed by multiple ellipses and smooth polygons. The smooth polygons are generated by aggregating the linear constraints that define the polygon into a single constraint, using a smoothened maximum function. Our general method also allows packing non-convex sets which are composites of ellipses and smooth polygons. The objective function in such problems defines the size of the "container" region being packed. We cast the non-overlap condition for all pairs of packed objects as a minimization problem and use the method of Lagrange multipliers to generate the non-overlap constraints. We present a concise summary of our approach, followed by a selection of packing challenges solved numerically.

Fitting seasonal influenza epidemic curves to surveillance: Application to the French Sentinelles network
Edward Thommes
Predicting the course of an influenza season is a long-standing challenge in biomathematical modeling, and the subject of an extensive body of research. Significant success has been achieved in fitting disease transmission models to surveillance data, both retrospectively and prospectively. However, choosing a level of model sophistication appropriate to the availability of data remains a tricky balancing act. Here, we report preliminary results from a particularly simple model. We begin by testing the ability of the model to accurately extract epidemic parameters from synthetic data, using both a simple Monte Carlo sweep and an optimization approach. We demonstrate the ability of the model to simultaneously recover the onset time, effective reproduction number, and under-reporting factor. We then apply our model to retrospective French surveillance data at both the national and regional level, obtained from the Réseau Sentinelles (Sentinel Network) site, http://www.sentiweb.fr/. Funding statement: ET, AC, LC, JL, TS are employees of Sanofi Pasteur. AA, SA, MG, JH, ZM, YX and JW have received funding from Sanofi Pasteur through a research grant.

A real-time optimization with warm-start of multiperiod AC optimal power flows
Youngdae Kim
We present a real-time optimization strategy combined with warm-start for a rolling horizon method applied to multi-period AC optimal power flow problems (MPACOPFs). In each horizon, ACOPFs are temporally inter-linked via ramping constraints, and we assume that each horizon needs to be solved in every few seconds or minutes. An approximate tracking scheme combined with two warm-start methods will be described. Our scheme closely follows the solution path consisting of strongly regular points. Theoretical results bounding the tracking error to the second order of the parameter changes of a single time period will be presented. Experimental results over various sizes of network up to 9k-bus will be given showing fast computation time of our method while maintaining a good solution quality, thus making it best suited to working under a real-time environment.

Computing and Calibrating Prices for Locational Variability in Power Generation and Load
Bernard Lesieutre
Fluctuations in variable power generation (e.g. wind and solar) and load are met in real-time using automatic generation control (AGC). The resources that respond to AGC control are chosen using a competitive market. In typical power systems, the costs for providing this power tracking service is shared among users, but is not weight more for those causing the variations. We cast the problem of procuring AGC resources as a chance-constrained optimization problem and calculate a locational price of variability. In this paper we consider how this locational price of variability might be calibrated to aid in computing charges for variability and for making payments to AGC resources. This approach will allocate higher prices for power fluctuations at locations for which it is difficult to accommodate variations, and lower prices at locations where it is easier to do so.

Improving an optimization problem by redatuming via a TRAC approach
Franck Assous
Parameter estimation plays a crucial role in imaging whether in the medical field or in seismic exploration, and remains an active subject of research, with many applications such as tumor detection or stroke prevention in the case of medical imaging. In geophysics, seismic imaging is used as a tool for exploring subsoil for oil, gas or other deposits. From the mathematical point of view, parameter estimation can be written as a PDE-constrained optimization problem, which tries to minimize the misfit between the recorded data and the reconstruction obtained by an estimated parameter. At each step of the optimization process, this estimation is updated to get closer to the original parameter to recover. In this context, it is well-known that the closer one is to the location of the parameter, the easier is the mathematical, and so the numerical, problem to solve. For this reason, the literature on this subject is large, since any method moving virtually the recording boundary closer to the parameter area, can be useful. Classical approaches generally solve least square problems based on paraxial approximations. In this spirit, we propose here a novel method that works directly in the time-dependent domain, and use the full wave equation. Note that it can be extended to other propagation problems, like for instance elastodynamics (elastic wave equation) or electromagnetism (Maxwell's equations). It basically combines an optimization method with the time-reversed absorbing condition (TRAC) method we introduced several years ago, that couples time-reversal techniques and absorbing boundary conditions. Mainly, we aim at reducing the size of the computational domain: in that sense, this can be related to redatuming method, that allows to reduce the size of the optimization problem, by moving virtually the recorded boundary. In our talk, we will describe our approach and illustrate its efficiency on numerical examples.

Impact of influenza vaccine-modified susceptibility and infectivity on the outcomes of immunization
Kyeongah Nah
To help informing vaccine manufacturers and individuals at high risks of developing serious flu-related complications, we develop compartmental models to assess the impact of vaccinating the population by different types of vaccines. In this talk, I will present the balance between vaccine-modified susceptibility, infectivity and recovery needed in preventing an influenza outbreak, or in mitigating the health outcomes of the outbreak using the SIRV-type of disease transmission model. We will also observe the impact of influenza vaccination program on the infection risk of vaccinated and non-vaccinated individuals.

Decision making of the population under media effects and spread of Influenza
Safia Athar
Media plays a vital role in controlling the decision making of the population in an epidemic. Influenza, a disease that affects every age group and causes mortality in many cases, is always a concern for public health. Role of mass-media reports on Influenza is studied in J. Heffernan.et.al. In the referred paper, the authors employed a stochastic agent-based model to provide a quantification of mass media reports on the variability in crucial public health measurements. In [M. Cojocaru, et.al.], the authors used the replicator dynamics to study the player's optimal strategy over time. In this research, we are studying the decision making of the population under the effects of media reports and how their decisions contribute to the control of influenza epidemic. For the purpose, we use Replicator equations to quantify the decision making of the population under the effect of disease and mass media reports. We adapted the model given by J. Heffernan.et.al and modified it by adding sub-compartments to susceptible and vaccinated compartments. We study the movement of population between these sub-compartments under the media effects in the presence of risk of getting an infection, and how these movements contribute to the incidence rate.

Stability and robustness of feedback based optimization for the distribution grid
Marcello Colombino
Feedback-based online optimization algorithms have gained traction in recent years because of their simple implementation, their ability to reject disturbances in real time, and their increased robustness to model mismatch. While the robustness properties have been observed both in simulation and experimental results, the theoretical analysis in the literature is mostly limited to nominal conditions. In this work, we propose a framework to systematically assess the robust stability of feedback-based online optimization algorithms. We leverage tools from monotone operator theory, variational inequalities and classical robust control to obtain tractable numerical tests that guarantee robust convergence properties of online algorithms in feedback with a physical system, even in the presence of disturbances and model uncertainty. The results are illustrated via an academic example and a case study of a power distribution system.

Modeling Hessian-vector products in nonlinear optimization
Lili Song
In this paper, we suggest two ways of calculating quadratic models for unconstrained smooth nonlinear optimization when Hessian-vector products are available. The main idea is to interpolate the objective function using a quadratic on a set of points around the current one and concurrently using the curvature information from products of the Hessian times appropriate vectors, possibly defined by the interpolating points. These enriched interpolating conditions form then an affine space of model or inverse model Hessians, from which a particular one can be computed once an equilibrium or least secant principle is defined. A first approach consists of recovering the Hessian matrix satisfying the enriched interpolated conditions, from which then a Newton approximate step can be computed. In a second approach we pose the recovery problem in the space of inverse model Hessians and calculate an approximate Newton direction without explicitly forming the inverse model Hessian. These techniques can lead to a significant reduction in the overall number of Hessian-vector products when compared to the inexact Newton method, although their expensive linear algebra make them only applicable to problems with a small number of variables.

Novel efficient algorithm for risk-set sampling in cohort studies of large administrative health databases
Salah Mahmud Christiaan Righolt
Large ($N > 10^6$) cohort studies can be efficiently analyzed with minimal loss of statistical power by sampling a smaller risk set from the study population. The risk set consists of all events of interest that occurred over a specified period of time (observation time) and an appropriate set of randomly selected controls individually matched to each event — typically on length of observation time and other important confounding (lurking) variables. It can be shown that the resulting association statistics estimated by fitting conditional logistic regression models to the matched sample are equivalent to the corresponding estimates using the entire cohort with loss of power not exceeding 10% for most scenarios when the sampling ratio is larger than 4. However, existing algorithms for risk-set sampling are computationally intensive and are often impractical when both the number of events and the cohort size are large which is usually the case in cohort studies of common conditions based on large administrative health databases. They are also not suitable for matching on time-varying variables. We developed a new algorithm, presently implemented in SAS, to efficiently match on both time-varying and time-independent variables in large databases. Improved efficiency is obtained by combining a new random sampling technique with a flexible matching procedure based on a user-defined cost function. The new sampling technique also simplifies matching on time-varying variables. We show using simulated datasets that the new algorithm produces valid statistical estimates, and compare its time, memory and CPU performance and resource utilization to those of the most efficient available algorithm (based on SAS’s hash tables).

Detecting Organ Failure in Motor Vehicle Trauma Patients: A Machine Learning Approach
Neil Deshmukh
Motor vehicle accidents are prevalent throughout the U.S.; over five million crashes occur each year. Typically, patients are appropriately diagnosed only after being transported to nearby medical centers, which currently takes about 7-15 minutes on average. This project aims to expedite this diagnostic process by training neural networks on Intensive Care Unit (ICU) data to automate the identification of injuries caused by motor vehicle accidents. Data was aggregated from the Beth Israel Deaconess Medical Center in Boston, Massachusetts via the Medical Information Mart for Intensive Care III (MIMIC-III) database, for patients' electrocardiogram (ECG) and respiratory rate reports. Natural Language Processing was used to isolate the patients of interest and classify them based on the area of injury, i.e., any of eight combinations of the three vital organs: brain, heart, and lungs. Upon isolation of the waveform data, noise was filtered via normalization, Butterworth and forward-backward filter application, and Fast Fourier transformation. The trained Artificial Neural Network (ANN) contained 23 dense layers with the number of neurons decreasing per two layers with ReLU activation and 10\% dropout. Multiclass activation was used for the final layer, in order to allow training for detection of multiple areas of trauma. The trained Convolutional Neural Network (CNN) had 12 convolutions, utilizing batch normalization, six pooling, one flatten, and two dense layers. Both models used AdamOptimizer. The CNN and ANN produced F1 scores of 0.82 and 0.56 respectively, suggesting the models could potentially perform accurate early detection of injury area and expedite hospital treatment of trauma patients.

Algorithms for Optimal Design and Operation of Networked Microgrids
Harsha Nagarajan
In recent years, microgrids, i.e., disconnected distribution systems, have received increasing interest from power system utilities to support the economic and resiliency posture of their systems. The economics of long distance transmission lines prevent many remote communities from connecting to bulk transmission systems and these communities rely on off-grid microgrid technology. Furthermore, communities that are connected to the bulk transmission system are investigating microgrid technologies that will support their ability to disconnect and operate independently during extreme events. In each of these cases, it is important to develop methodologies that support the capability to design and operate microgrids in the absence of transmission over long periods of time. Unfortunately, such planning problems tend to be computationally difficult to solve and those that are straightforward to solve often lack the modeling fidelity that inspires confidence in the results. To address these issues, we first develop a high fidelity model for design and operations of a microgrid that include component efficiencies, component operating limits, battery modeling, unit commitment, capacity expansion, and power flow physics; the resulting model is a mixed-integer quadratically-constrained quadratic program (MIQCQP). We then develop an iterative algorithm, referred to as the Model Predictive Control (MPC) algorithm, that allows us to solve the resulting MIQCQP. We show, through extensive computational experiments, that the MPC-based method can scale to problems that have a very long planning horizon and provide high quality solutions that lie within 5% of optimal.

Adaptive randomized rounding in the big parsimony problem
SANGHO SHIM
A phylogenetic tree is a binary tree where each node represents a sequence of the states and all the input sequences are represented at the leaf nodes. Given sequences of the states of the same length, the big parsimony problem constructs the most parsimonious phylogenetic tree along with labeling the internal nodes at the maximum parsimony. The big parsimony problem is known to be NP-hard. We describe randomized rounding methods that allow us to obtain good solutions. Our first randomized rounding method starts with a fractional optimal solution to the LP-relaxation of an integer linear programming formulation of the big parsimony problem, and repeats randomized rounding based on this fractional solution, which we refer to as fixed ran-domized rounding without changing the fractional solution. Solutions obtained using the fixed randomized rounding approach are superior to the best solutions obtained using branch-and-bound with GUROBI and can be obtained quicker. We then describe an adaptive randomized rounding approach where the underlying fractional solution changes based on the best integer solution observed so far and produces solutions that are superior to the fixed randomized rounding approach.

The role of pneumonia/influenza in hospital readmissions: Burden and predictive factors via machine learning
Secil Sozuer
The Hospital Readmissions Reduction Program (HRRP) was established by the 2010 Affordable Care Act. This program requires the Centers for Medicare and Medicaid Services to reduce the reimbursements to hospitals with excessive readmissions. HRRP defines these as an admission for any cause (“all-cause readmission”) occurring 30 days or less after an initial (“index”) admission falling into one of several specified categories. Due to this program, readmissions are considered as a quality benchmark for health systems. Here, we will discuss our work and methodology on characterizing the contribution of pneumonia and influenza (P&I) to the burden of readmissions among a population of Medicare Advantage patients aged 65 and over. For the index admission, we apply the same inclusion/exclusion criteria for codes and diseases as the Centers for Medicare and Medicaid Services. We calculate probabilities of P&I readmission after an index admission in the following HRRP categories : Acute myocardial infarction (AMI), 2.0%; congestive heart failure (CHF), 3.0%; chronic obstructive pulmonary disease (COPD), 3.8%; type II diabetes, 1.6%. For comparison, the overall probability of readmission (all-cause readmission within 30 days of an all-cause index admission) is 13%, and the probability of P&I readmission following an all-cause index admission is 1.5%. We will also present preliminary work on the construction of machine learning algorithms for identifying individuals at risk for P&I readmission. Predictive performance is measured by the area under the curve of the receiver operating curve (AUC-ROC). Funding statement: EWT and AC are employees of Sanofi Pasteur. SS is paid by Sanofi Pasteur through an internship program.

Regularized Robust Optimization for Two-Stage Stochastic Programming
Mingsong Ye
Two-stage stochastic optimization problems with parameter uncertainty are ubiquitous in many applications. Coordinating distributed energy resources with intermittent capacities is an example of this class of problems. Robust optimization is a recently popular approach to deal with uncertainty in optimization. In this method, a feasible solution with the best worst-case performance with respect to an uncertainty set is sought. The typical assumption there is that the decision maker can accurately provide the uncertainty set. In this paper, we first analyze the stability and sensitivity of robust two-stage stochastic optimization problems considering general perturbations of the uncertainty set with respect to the Hausdorff distance. We then present a regularized robust optimization using the new concept of regularized uncertainty set and establish the stability of the new approach. Solving the robust counterpart problem with the regularized uncertainty set is discussed.

Enabling A Stochastic Wholesale Electricity Market Design
Yury Dvorkin
Efficiently accommodating uncertain renewable and demand-side resources in wholesale electricity markets is among the foremost priorities of market regulators in the US, UK and EU nations. However, existing deterministic market designs fail to internalize the uncertainty and their scenario-based stochastic extensions are limited in their ability to simultaneously maximize social welfare and guarantee non-confiscatory market outcomes in expectation and per each scenario. This paper propose a chance-constrained stochastic market design, which is capable of producing a robust competitive equilibrium and internalizing uncertainty of the renewable and demand-side resources in the price formation process. The equilibrium and resulting prices are obtained for different uncertainty assumptions, which requires using either linear (restrictive assumptions) or second-order conic (more general assumptions) duality in the price formation process. The usefulness of the proposed stochastic market design is demonstrated via the case study carried out on the 8-zone ISO New England testbed.

The Inmate Transportation Problem and its Application in the PA Department of Corrections
Anshul Sharma
The Inmate Transportation Problem (ITP) is a common complex problem in any correctional system. We develop a weighted multi-objective mixed integer linear optimization (MILO) model for the ITP. The MILO model optimizes the transportation of the inmates within a correctional system, while considering all legal restrictions and best business practices. We test the performance of the MILO model with real datasets from the Pennsylvania Department of Corrections (PADoC) and demonstrate that the inmate transportation process at the PADoC can significantly be improved by using operations research methodologies.

A further study on the trajectory sensitivity analysis of controlled-prescription opioid epidemic dynamical models
Getachew Befekadu
In the context of a mathematical model describing prescription opioid epidemics, we consider a general formalism of trajectory sensitivity study that complements time-domain simulation in the analysis of nonlinear dynamic behaviors of a controlled-prescription opioid epidemic model. In particular, we perform linearization around a nonlinear, and possibly showing non-smooth, trajectory and study further the influence of parameter variations on the prescription opioid epidemic dynamics from the estimated sensitivities analysis with respect to extra controlling or intervening parameters - where such large (or small) trajectory sensitivities generally indicating that these extra-parameters have significant (or negligible) effects on the opioid epidemic dynamical behavior. Moreover, the insights we get from such trajectory sensitivities studies are useful in analyzing the underlying influences on system behavior dynamics, as well as assessing the significance or consequence to parameter uncertainties. Finally, as an illustrative example, we presented some simulation results that demonstrated the advantages and usefulness of the proposed trajectory sensitivities study using literature-based parameters associated with a typical prescription opioid epidemics. (Joint work with Christian Emiyah and Kofi Nyarko, Department of Electrical & Computer Engineering, Morgan State University).

Virtual Network Function placement optimization with Deep Reinforcement Learning
Ruben Solozabal
Network Function Virtualization (NFV) introduces a new network architecture framework that evolves network functions, traditionally deployed over dedicated equipment, to software implementations that run on general-purpose hardware. One of the main challenges for deploying NFV is the optimal resource placement of demanded network services in the NFV infrastructure. The virtual network function placement and network embedding can be formulated as a mathematical optimization problem concerned with a set of feasibility constraints that express the restrictions of the network infrastructure and the services contracted. This problem has been reported to be NP-hard, as a result most of the optimization work carried out in the area has been focused on designing heuristic and metaheuristic algorithms. Nevertheless, in highly constrained problems, as in this case, these methods tend to be ineffective. In this sense, an interesting solution is the use of Deep Neural Networks to model an optimization policy. The work presented here extends the Neural Combinatorial Optimization theory by considering constraints in the definition of the problem. The resulting agent is able to learn placement decisions exploring the NFV infrastructure aiming to minimize the overall power consumption. Conducted experiments demonstrate that the proposed strategy outperforms Gecode solver when solutions need to be obtained within a limited time-frame.

Coupling Artificial Neural Networks with Chance Constrained Optimization for Voltage Regulation in Distribution Grids
Nikolaos Gatsis
Electricity distribution grids are envisioned to host an increasing number of photovoltaic (PV) generators. PV units are equipped with inverters that can inject or absorb reactive power, a capability that can be crucial for enabling adequate voltage regulation. This talk deals with an optimal power flow (OPF) formulation including probabilistic specifications that nodal voltages remain within safe bound. The chance constraints are approximated by the conditional value at risk. The solution of the resulting OPF yields optimal inverter set points for a set of uncertainty realizations. These are subsequently treated as training scenarios for an artificial neural network corresponding to each PV inverter. The objective of each ANN is to produce the reactive power setpoints corresponding to other realizations of the uncertainty in real time and in a decentralized fashion. The overall design is tested on standard test feeders and the voltage regulation capability is numerically analyzed.

On the (near) Optimality of Extended Formulations for Multi-way Cut in Social Networks
SANGHO SHIM
In the multiway cut problem we are given an edge-weighted graph and a subset of the nodes called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the min cut max flow problem, and can be solved in polynomial time. This problem is known to be NP-hard as soon as k = 3. Among practitioners, an integer programming formulation of the problem introduced by Chopra and Owen (Mathematical Programming 73 (1996) 7-30) is empirically known to be strong on a social network, which is usually tree-like and almost planar. (We refer to the formulation as EF2 following the authors.) In particular, EF2 is very strong when the edge weights are equally likely and we study the cardinality minimum multiway cut problem (i.e., the edge weights are all 1). We explore the max flow in the cardinality minimum multiway cut problem and show that the cardinality EF2 on a wheel graph has a primal integer solution and a dual integer solution of the same value. We consider a hub-spoke network of wheel graphs constructed by adding to the wheel graphs the edges of a hub graph which consists of the hub nodes of the wheel graphs and edges connecting the hub nodes. We assume that every wheel has a terminal hub or a terminal node with three non-terminal neighbors, and show that if the hub graph is planar, the cardinality EF2 on the hub-spoke network of the wheel graphs has a primal integer solution and a dual integer solution of the same value. An algorithm developed by Chrobak and Eppstein (Theoretical Computer Science 86 (1991) 243-266) is modied and used for the proof.

Optimal design of vaccination catchup programswith incentives
Monica Cojocaru Kevin Fatyas
Vaccines work by creating an immune response to various illnesses by stimulating the body's immune system. Immunization overall has yielded positive results, and has proven to be a cost-effective solution to disease prevention that ultimately improves quality of life. For newer and relatively more expensive vaccines, the decision to include these vaccines in publicly funded immunization programs largely depends on demand for the product and a willingness for taxpayers to seek out these types of health benefits. We present here a simple implementation scenario, once a recommendation for the introduction of a vaccine in a target population is made: how to best invest public funds, to achieve two concurrent goals: minimize the cost of the program and maximize the overall vaccination coverage for a given budget?

Quasi-Newton Methods for Deep Learning: Forget the Past, Just Sample
Martin Takac
We present two sampled quasi-Newton methods for deep learning: sampled LBFGS (S-LBFGS) and sampled LSR1 (S-LSR1). Contrary to the classical variants of these methods that sequentially build Hessian or inverse Hessian approximations as the optimization progresses, our proposed methods sample points randomly around the current iterate at every iteration to produce these approximations. As a result, the approximations constructed making use of more reliable (recent and local) information and do not depend on past iterate information that could be significantly stale. We also show that these methods can be efficiently implemented in a distributed computing environment.

Learning Methods for Distribution System State Estimation
Ahmed Zamzam
Distribution system state estimation (DSSE) is a core task for monitoring and control of distribution networks. Widely used Gauss-Newton approaches are not suitable for real-time estimation, often require many iterations to obtain reasonable results, and sometimes fail to converge. Learning-based approaches hold the promise for accurate real-time estimation. This talk presents a data-driven approach to `learn to initialize' -- that is, map the available measurements to a point in the neighborhood of the true latent states (network voltages), which is used to initialize Gauss-Newton. In addition, a novel physics-aware learning model is presented where the electrical network structure is utilized to parametrize a deep neural network. The proposed neural network architecture reduces the number of trainable coefficients needed to realize the mapping from the measurements to the network state by exploiting the separability of the estimation problem. This approach is the first that leverages electrical laws and grid topology to design the neural network for DSSE. We also show that the developed approaches yield superior performance in terms of stability, accuracy, and runtime, compared to conventional optimization-based solvers.

Simulation-Based Optimization of Dynamic Appointment Scheduling Problem with Patient Unpunctuality and Provider Lateness
Secil Sozuer
Healthcare providers are under growing pressure to improve efficiency due to an aging population and increasing expenditures. This research is designed to address a particular healthcare scheduling problem, dynamic and stochastic appointment scheduling with patient unpunctuality and provider lateness. We consider that the stochasticity is coming from uncertain patient requests, uncertain service duration, patient unpunctuality and provider lateness amount. The aim is to find the optimal schedule start time for the patients in order to minimize the expected cost incurred from patient waiting time, server idle time, and server overtime. By conducting perturbation analysis for the gradient estimation, a Sample Average Approximation (SAA) and a Stochastic Approximation (SA) algorithm are proposed. The structural properties of the sample path cost function and expected cost function are studied. Numerical experiments show the computational advantages of SAA and SA over the mathematical model.

An Epidemics-Logistics Modeling Framework: Insights into Controlling the Ebola Virus Disease in West Africa
Esra Buyuktahtakin Toy
In this study, we address a core limitation of existing epidemiological models by introducing a new epidemics-logistics mixed-integer programming (MIP) formulation to determine the optimal amount, timing and location of resources that are allocated for controlling an epidemic. The present study is the first spatially explicit optimization approach that considers geographically varying rates for disease transmission, migration of infected individuals over different regions, and varying treatment rates due to the limited capacity of treatment centers. We illustrate the performance of the MIP model using the case of the 2014-2015 Ebola outbreak in Guinea, Liberia, and Sierra Leone.

Derivative Approximation of some Model-based Derivative Free Methods
Liyuan Cao
To optimize a black-box function, gradient-based methods can be used in conjunction with finite difference methods. Alternatively, optimization can be done with polynomial interpolation models that approximate the black-box function. A class of random gradient-free algorithms based on Gaussian smoothing of the objective function was analyzed by Yurii Nesterov in 2011. Similar random algorithms were implemented and discussed in the machine learning community in more recent years. We compare these methods on their accuracy of gradient approximation and the overall performance.

Convex Restrictions for Optimal Power Flow
Line A. Roald
The optimal power flow is an optimization problem commonly solved in operation of electric power systems, and obtaining tight convex relaxations (i.e., good convex outer approximations) of this problem has recently received significant attention. However, since power systems are critical infrastructure, ensuring safe operations is of paramount importance. In particular, ensuring that there exist a feasible solution to the non-convex equality constraints representing the AC power flow equations is a challenge. In this talk, we describe convex restrictions, which represent safe convex inner approximations of the optimal power flow feasible region. We discuss how this allows us to solve robust AC optimal power flow and guarantee feasible system trajectories.

Generalized Nonconvex Relaxations to Rank Minimization
April Sagan
Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective technique at solving the problem with strong performance guarantees. However, nonconvex relaxations have the capability of solving the rank minimization problem in cases with less measurements than required for exact rank minimization via nuclear norm minimization and in less time. We develop efficient algorithms utilizing the low rank factorization for semidefinite programs put forth by Burer and Monteiro and show computational results demonstrating the advantages over convex relaxations and alternating minimization methods. Additionally, each iteration of our algorithm is less expensive by O(n) operations for an nxn matrix when compared to similar approaches, allowing us to quickly find solutions to rank minimization for large matrices.

A Multi-Stage Stochastic Programming Approach to Controlling the Ebola Virus Disease with Equity Considerations
Xuecheng Yin
The optimization of resource allocation for controlling an epidemic outbreak is one big limitation in existing compartmental models. In this study, we formulate the resource allocation problem while forecasting the progression of the disease as a multi-stage stochastic programming epidemic compartmental model. In this model, based on an available budget we formulate spatio-temporally varying treatment rate. This model is applied to study the case of Ebola Virus Disease in West Africa to minimize an overall expected number of infected individuals, considering possible infection scenarios. We also consider equity constraints in order to allocate resources more fairly to three impacted countries in West Africa. Our model is practical and can be adopted to study other infectious diseases in complex situations.

Optimal Decision Trees for Categorical Data via Integer Programming
Minhan Li
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if allowed to grow large, they lose interpretability. In this paper, we present a novel mixed integer programming formulation to construct optimal decision trees of a prespecified size. We take the special structure of categorical features into account and allow combinatorial decisions (based on subsets of values of features) at each node. We show that very good accuracy can be achieved with small trees using moderately-sized training sets. The optimization problems we solve are tractable with modern solvers.

Applications of Constraint Screening Methods in Electric Power Systems
Dan Molzahn
In many power system optimization problems, it is often observed that only a small fraction of the constraints ever become binding at the optimal solution, despite variations in the load profile and generation costs. This observation has far-reaching implications not only for power system optimization, but also for the practical long-term planning, operation, and control of the system. Formalizing this observation, constraint screening methods characterize the set of constraints that may potentially be binding over a range of problem parameters. This presentation describes two applications of constraint screening methods. The first application identifies redundant line flow limits whose elimination can significantly improve the computational tractability of unit commitment problems. The second application is an algorithm that determines when so-called grid-agnostic controllers, which neglect engineering constraints, can be applied without concern regarding network constraint violations.

Nonlinear regularization for solving non-linear inverse problems
Dimitri Papadimitriou
Neural parameter learning (or parameter/system identification) belong to the class of nonlinear inverse problems. These are ill-posed problems in the Hadamard sense: they require reformulation for numerical processing otherwise existence, uniqueness and stability upon input data variation can't be guaranteed. This method is known as regularization. Let $F(u) = y^{\delta}$ denote the nonlinear inverse/ill-posed problem, where $F$ is a nonlinear operator and $y^{delta}$ noisy samples of $y$ such that $\left\|y – y^{delta}\right\| \leq \delta$, for some noisy level $\delta > 0$. Constructing a (variational) regularization for nonlinear inverse problems of this form consists of finding two functionals: a data fidelity term $E$ (e.g., quadratic fidelity) measuring the distance between $F(u)$ and $y^{\delta}$, and a regularization functional $R$ favoring appropriate minimizers or penalizing potential solutions with undesired structures. A key question in this respect is the convergence for noisy data, related to the choice of the regularization parameter $\alpha$ in dependence on the noise level $\delta$. With too little regularization, the regularized approximations $u_{\alpha}^{\delta}$ -that minimizes the total error, a.k.a. generalized Tikhonov functional- are highly oscillatory due to noise amplification whereas with too much regularization, the regularized approximations are too close to the initial guess $u^{*}$. Thus, one should select the regularization parameter such that the total error $\left\|u_{\alpha}^{\delta} – u^{*}\right\|$ is minimized. Though using the term regularization in much broader sense than its formal definition of regularization (with stability, convergence and efficiency criteria), many experimental papers show that some linear regularization functionals don't explain or improve the properties of the minimizer of the Tikhonov functional. However, regularization covers also non-quadratic ($L_p, 0 < p \leq 1$) and total variation functionals (TV-Regularization). In this paper, we demonstrate how TV-functionals combined with iterative regularization yields a competitive method for the solving of nonlinear inverse problems yields. The gain compared to Tikhonov regularization is illustrated by numerical examples.

Optimizing Search and Control of EAB in Canadian Forests
Sabah Bushaj
Emerald Ash Borer (EAB) is a wood-boring invasive insect, which is native to Asia causing extensive damage to ash trees in North America. EAB was discovered in 2002 near Detroit and since its accidental introduction, it has destroyed millions of ash trees in the United States and Canada. Current studies on EAB spread have estimated an enormous economic cost to the Canadian street and backyard trees. Some insecticides have shown to be effective in curing and protecting ash trees from EAB. Possible actions include surveillance, treatment, and removal of ash trees. We study a multistage stochastic mixed-integer programming (M-SMIP) model to optimize the surveillance, treatment and removal decisions over a limited budget. We maximize public benefits by optimally allocating resources to surveillance and control of EAB spread. We calibrate a formerly validated model of ash dynamics with a new dispersal mechanism and apply the optimization model to the city of Winnipeg in the province of Manitoba, Canada. Due to the inability to survey a vast amount of ash trees, we present a more efficient way to predict the dispersal of the invasive species.

Limited-Memory BFGS with Displacement Aggregation
Baoyu Zhou
We present a displacement aggregation strategy for the curvature pairs stored in a limited-memory BFGS method such that the resulting (inverse) Hessian approximations are equal to those derived from a full-memory BFGS method. Using said strategy, an algorithm employing the limited-memory method can achieve the same convergence properties as when full-memory Hessian approximations are employed. We illustrate the performance of an L-BFGS algorithm that employs the aggregation strategy.

False data injection attack in coordinated natural gas and electricity systems
Bining Zhao
The increased penetration of natural gas-fired generation units in electricity systems calls for coordination of gas and electricity systems. Notably, both energy systems are vulnerable to malicious cyber-attacks. Within this context, we propose a coordination scheme for the day-ahead schedule of gas and electricity systems. We define a new class of false data injection (FDI) cyber-attacks on the exchanged information between the two systems, and investigate the impacts of such attacks on the operation of both energy systems. The coordination mechanism consists of three nested optimization problems. With consideration of attacks, the gas-scheduling step in the mechanism is modeled as a bi-level max-min optimization problem, and a column and constraint generation (C&CG) algorithm is used to solve this bi-level problem. The coordination mechanism and bi-level attack problem are examined using a case study based on the IEEE 24-node test system and a 9-node gas system.

Computational Optimization for Nonimaging Solar Concentrators using Generalized Pattern Search
Christine Hoffman
We present a computational framework for optimizing nonimaging solar concentrators. Our approach is to represent the concentrator’s shape as a polygon, use ray tracing to compute the flux at the receiver, and employ a derivative-free optimization, Generalized Pattern Search (GPS), on the polygon’s vertices. Many shape optimization techniques use gradients to seek a direction of steepest ascent or descent. For solar concentrators, these approaches can easily get trapped in local minima. In contrast, GPS is a derivative-free method that seeks a global optimum on suitable meshes, without computing gradients. This helps to avoid getting trapped in local minima. Results for 2D concentrators show that our algorithm can converge to the ideal concentrator's shape as the number of polygon vertices increases. We also show that when the number of vertices is small and fixed, the optimal polygon can differ significantly from the polygon that would be obtained using a uniform collocation of the ideal shape. Uncertainty quantification is used to determine design efficiency robustness. This approach could lead to a simple, accurate, and fast design method, and improve the performance and lower the fabrication costs of nonimaging concentrators for solar and thermal applications.

Achieving Acceleration in Distributed Optimization via Direct Discretization of the Heavy-Ball ODE
Cesar A. Uribe
We develop a distributed algorithm for convex Empirical Risk Minimization,the problem of minimizing large but finite sum of convex functions over networks. The proposed algorithm is derived from directly discretizing the second-order heavy-ball differential equation and results in an accelerated convergence rate, i.e, faster than distributed gradient descent based methods for strongly convex objectives that may not be smooth. Notably, we achieve acceleration without resorting to the well-known Nesterov’s momentum approach. We provide numerical experiments and contrast the proposed method with recently proposed optimal distributed optimization algorithms.

Decomposable Formulation of Transmission Constraints for Decentralized Power Systems Optimization
Alinson Santos Xavier
When solving large-scale power systems optimization problems, such as the Day-Ahead Security-Constrained Unit Commitment Problem (DA SCUC), one of the most complicating factors is modeling transmission and security constraints. The most common formulation used in the industry, based on Injection Shift Factors (ISF), yields very dense and unstructured constraints, which not only may cause performance issues, but also makes it unsuitable for decentralized studies, such as optimal energy exchange. In this work, we present a novel DC power flow formulation which has a decomposable block-diagonal structure, scales well for large systems, and can efficiently handle N-1 security requirements. Benchmarks on Multi-Zonal Security-Constrained Unit Commitment problems show that the proposed formulation can reliably and efficiently solve instances with up to 6,515 buses, with no convergence or numerical issues.

Warranty of kinematic stability in truss topology design optimization
Mohammad Shahabsafa
In this work, we propose a novel mathematical optimization model for the discrete Truss Topology Design and Sizing Optimization (TTDSO) problem with Euler buckling constraints. Our model is significantly more efficient, from a computational point of view, than previously published models. Random perturbations of external forces are used to obtain kinematically stable structures. We formally prove that by considering the perturbed external forces, the resulting structure is kinematically stable with probability one. Furthermore, we show that necessary conditions for kinematic stability can be used to speed up the solution time of TTDSO problem. Numerical results demonstrate that our model can be solved significantly faster than other discrete TTDSO models introduced before.

An Efficient Method to find approximate Solutions to Linear and Nonlinear Fractional Differential Equations via Fractional Natural Decomposition Method
Mahmoud Alrawashdeh
In this talk, we implement a new method called the Fractional Natural Decomposition Method (FNDM) to solve different types of fractional linear and nonlinear differential equations. Also, we present approximate solutions to two systems of fractional linear ordinary differential equations. Most of the graphs were performed using Mathematica software. The study outlines the significant features of the FNDM. The results have shown that the FNDM is very efficient, convenient and can be applied to a large class of linear and nonlinear fractional differential equations. One can conclude that the method is easy to use and efficient

Tight Piecewise Convex Relaxations for Global Optimization of Optimal Power Flow
Harsha Nagarajan
Since the alternating current optimal power flow (ACOPF) problem was introduced in 1962, developing efficient solution algorithms for the problem has been an active field of research. In recent years, there has been increasing interest in convex relaxations-based solution approaches that are often tight in practice. Based on these approaches, we develop tight piecewise convex relaxations with convex-hull representations, an adaptive, multivariate partitioning algorithm with bound tightening that progressively improves these relaxations and, given sufficient time, converges to the globally optimal solution. We illustrate the strengths of our formulations and algorithms using extensive benchmark ACOPF test cases from the literature. Computational results show that our novel algorithm reduces the best-known optimality gaps for some hard ACOPF cases.

Solving Large-scale Multi-scenario Truss Sizing Optimization Problem
Ramin Fakhimi
Discrete multi-scenario truss sizing problems are very challenging to solve due to their combinatorial, nonlinear, non-convex nature. Consequently, multi-scenario truss sizing problems become unsolvable as the size of the truss grows. We consider various mathematical formulations for the truss design problem with the objective of minimizing weight, while the cross-sectional areas of the bars take only discrete values. Euler buckling constraints, Hooke's law, and bounds for stress and displacements are also considered. We extend the Neighborhood Search Mixed Integer Linear Optimization (NS-MILO) approach to solve large-scale multi-scenario discrete truss design problems and demonstrate that the NS-MILO approach provides high-quality solutions for large-scale real multi-scenario truss sizing problems.

Recent Innovations for the Projective Splitting Algorithm
Patrick Johnstone
Projective splitting is a primal-dual operator splitting algorithm for solving finite-sum convex optimization problems and monotone inclusions. The method is highly flexible and supports asynchronous and distributed computation. In the last two years, we have developed several innovations for the method to do with making use of forward steps rather than only resolvent (i.e. proximal) calculations. Forward steps (i.e. explicit evaluations of an operator) are computationally easier than resolvents and usually more convenient to implement. In this talk, I will provide an overview of these innovations. I will then focus on the most recent progress: developing a projective splitting variant for cocoercive operators that uses a single forward step per iteration.

Mixed Integer Programming Formulations for the Unit Commitment Problem
Bernard Knueven
This work is a comprehensive overview of mixed integer programming formulations for the unit commitment (UC) problem. UC formulations have been an especially active area of research over the past twelve years due to their practical importance in power grid operations. Because of this work, researchers now have a much better understanding of the mathematical structure of the UC problem. However, this understanding does not necessarily lead to improved solution times. To better understand the relationship between computational performance and theoretical quality, we implemented and exhaustively tested many of the existing UC formulations in the literature on both academic and real-world data. We provide reference implementations of all formulations examined as part of the EGRET software package, publically available on GitHub.

A binary expansion method in finding a good lower bound of weight in truss sizing design
Weiming Lei
Continuous truss sizing problem has been widely researched. However, due to the complexity of structure and model, a solution is hard to be proved globally optimal. We introduce the binary expansion method in order to find a good lower bound in minimizing the weight of truss structure with certain topology and continuous cross-section area, so that to evaluate how close a solution is to be optimal. Hooke’s law, bounds for stress and displacements, and Euler buckling constraints are considered in our model. In our numerical experiment, the benchmark problem of 10, 25 and 72 bars are considered. The results show that the gap between the lower bound by binary expansion method and the upper bound of the original continuous problem given by IPOPT is less than 1%, which means both methods are close to optimal.

The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learning
Suyun LIU
Optimization of conflicting functions is of paramount importance in decision making, and real world applications frequently involve data that is uncertain or unknown, resulting in stochastic multi-objective optimization (MOO). In this paper, we study the stochastic multi-gradient (SMG) method, seen as a natural extension of the classical stochastic gradient method for single-objective optimization. At each iteration of the SMG method, a stochastic multi-gradient direction is calculated by solving a quadratic subproblem, and it is shown that this direction is biased even when all individual gradient estimators are unbiased. Our convergence analysis establishes rates to compute a point in the Pareto front, of order similar to what is known for stochastic gradient in both convex and strongly convex cases. The analysis handles the bias in the multi-gradient and the unknown a priori weights of the limit Pareto point. The SMG method is then framed into a Pareto-front type algorithm for the computation of the entire Pareto front. The Pareto-front SMG algorithm is capable of robustly determining Pareto fronts for a number of synthetic test problems. One can apply it to any stochastic MOO problem arising from supervised machine learning, and we report results for logistic binary classification where multiple objectives correspond to distinct-sources data groups.

Time-Varying Semidefinite Programs
Bachir El Khadir
We study time-varying semidefinite programs (TV-SDPs), which are semidefinite programs whose data (and solutions) are functions of time. Our focus is on the setting where the data varies polynomially with time. We show that under a strict feasibility assumption, restricting the solutions to also be polynomial functions of time does not change the optimal value of the TV-SDP. Moreover, by using a Positivstellensatz on univariate polynomial matrices, we show that the best polynomial solution of a given degree to a TV-SDP can be found by solving a semidefinite program of tractable size. We also provide a sequence of dual problems which can be cast as SDPs and that give upper bounds on the optimal value of a TV-SDP (in maximization form). We prove that under a boundedness assumption, this sequence of upper bounds converges to the optimal value of the TV-SDP. We demonstrate the efficacy of our algorithms on applications in optimization and control.

Optimizing Energy Storage Operation via Dual Decomposition
BOLUN XU
This talk introduces a novel dual decomposition method for the fast solution of multi-period energy storage control problems. The proposed method solves deterministic single storage control problems to optimal within milliseconds in all application scenarios regardless of the look-ahead horizon or the objective function form, offering significant improvements compared to using commercial optimization solvers. The talk will also introduce our current effort of applying this algorithm in optimizing battery operation under its degradation mechanism and for optimizing multiple storage operations.

Different approaches between Pattern Search Algorithm and Particle Swarm Optimization
Eric Koessler, Ahmad Almomani
Different approaches between Pattern Search Algorithm and Particle Swarm Optimization Eric Koessler and Ahmad Almomani Mathematics Department, State University of New York at Geneseo, Geneseo, NY, 14454June 30, 2019 Abstract Pattern Search (PS) are an important class of optimization algorithms which popular with researchers who use Derivative-Free Optimization (DFO). Particle Swarm Optimization (PSO) is one of the most commonly used stochastic optimization algorithms, and population based on the simulation of the social behavior of particles. In this talk, we introduce three approaches of hybridizing PS and PSO to improve the global minima and efficiency. Numerical results and parallel computing using the most known non-differentiable test functions reveal that all three methods improve the global minima and robustness versus PSO.

On Local Optimality in Cubic Optimization
Jeffrey Zhang
In this paper we examine local optimality in unconstrained cubic optimization. We give a characterization of when a point is a strict or nonstrict local minimum of a cubic polynomial, and show that it can be checked in polynomial time. We then address the problem of finding local minima of cubic polynomials.

A strong formulation for the graph partition problem
SANGHO SHIM
We develop a polynomial size extended graph formulation of the graph partition problem which dominates the formulation introduced by Chopra and Rao [Mathematical Programming 59 (1993) 87-115], and show that the extended graph formulation is tight on a tree. We introduce exponentially many valid inequalities to the Chopra-Rao formulation, which we call generalized arc inequalities, and develop a linear time algorithm to separate the most violated generalized arc inequality. We show that the polynomial size extended graph formulation is equivalent to the Chopra-Rao formulation augmented by the exponentially many generalized arc inequalities.

Design of neuro-evolutionary model for solving nonlinear singularly perturbed boundary value problems
Muhammed Syam
In this study, a neuro-evolutionary technique is developed for solving singularly perturbed boundary value problems (SP-BVPs) of linear and nonlinear ordinary differential equations (ODEs) by exploiting the strength of feed-forward artificial neural networks (ANNs), genetic algorithms (GAs) and sequential quadratic programming (SQP) technique. Mathematical modeling of SP-BVPs is constructed by using a universal function approximation capability of ANNs in mean square sense. Training of design parameter of ANNs is carried out by GAs, which is used as a tool for effective global search method integrated with SQP algorithm for rapid local convergence. The performance of the proposed design scheme is tested for six linear and nonlinear BVPs of singularly perturbed systems. Comprehensive numerical simulation studies are conducted to validate the effectiveness of the proposed scheme in terms of accuracy, robustness and convergence.

A decoupled first/second-order steps technique for nonconvex optimization
Clément Royer
Second-order properties are particularly useful in nonconvex optimization, as they can be used to provably avoid convergence towards low-quality solutions such as saddle points. For certain classes of nonconvex problems arising in data science, second-order conditions can even be shown to characterize global optima. Consequently, there has been a surge of interest in developing optimization algorithms with second-order guarantees. However, as enlightened by recent complexity analyses of some of these methods, the overall effort to approach second-order points is significantly larger compared to that of reaching first-order ones. Even more so, several frameworks originally designed with first-order convergence in mind, do not appear to maintain the same first-order performance when modified to incorporate second-order aspects. In this talk, we propose a technique that separately computes first- and second-order steps, with second-order convergence guarantees. The key idea consists in better connecting the steps to be taken and the stationarity criteria, which potentially leads to larger steps and decreases in the objective. As a result, we obtain an improvement of the complexity bound with respect to the first-order optimality tolerance, and this has a positive impact on the practical behavior. Although its applicability is wider, we present our concept within a trust-region framework based on exact and inexact derivatives. In this latter setting, we also reveal interesting connections between our technique and the criticality steps used in derivative-free optimization.

Using a Mobile Microgrid Formulation to Increase Smart Grid Resiliency
Brandon Augustino
We propose two models for the microgrid formation problem which have more capabilities than those currently in the literature. The first model is a standard microgrid formation problem, whereas the second is an extension in which we consider a road network, and the costs of restoring this road network after a disaster in order to dispatch distributed generators (DGs) to selected nodes for connection. Our models capture the DG location choice and microgrid formation problem as a mechanism to restore critical loads after some random event causes a major fault to a power system. Further, our formulation is shown to be able to consider mesh topologies. For the model without transportation, we provide benchmark results for the model using a modified IEEE 37-bus system and perform scalability analysis on the IEEE 85-bus and 141-bus systems. Additionally, we provide results on a modified IEEE 118-bus system, to evaluate the performance on our model with respect to mesh topologies. For the model with transportation considerations, we provide results using a modified IEEE 37-bus system. The first formulation requires fewer binary variables than other models in the literature. Consequently, the first proposed formulation scales very well with the number of nodes while also having more decision making capabilities, in addition to outperforming other models currently in the literature.