8:00 
9:00 
Registration and breakfast

9:00 
10:00 
Plenary talk
On big data, optimization and learning
Andrea Lodi
abstract
On big data, optimization and learning
Andrea Lodi
In this talk I review a couple of applications on Big Data that I personally like and I try to explain my point of view as a Mathematical Optimizer  especially concerned with discrete (integer) decisions  on the subject. I advocate a tight integration of Machine Learning and Mathematical Optimization (among others) to deal with the challenges of decisionmaking in Data Science. For such an integration I try to answer three questions: 1) what can optimization do for machine learning? 2) what can machine learning do for optimization? 3) which new applications can be solved by the combination of machine learning and optimization?


10:00 
10:15 
Coffee break

10:15 
11:45 
Parallel technical sessions
New Directions in Optimization and Dynamical Systems

Stochastic Optimization

Iterative Methods

Applications in Healthcare

Sparsity Still Matters
Robert Vanderbei
abstract
Sparsity Still Matters
Robert Vanderbei
In this talk, I will focus on one particular issue that permeates much of the
world of optimization, namely, the importance of understanding that ``modeling matters'' and, in particular, that exploiting sparsity in a problem's representation can be extremely beneficial.

LNG Supply Chain Planning Under Demand and Supply Uncertainty : A Stochastic Programming Formulation and Solution Strategy.
Armando Guarnaschelli
abstract
LNG Supply Chain Planning Under Demand and Supply Uncertainty : A Stochastic Programming Formulation and Solution Strategy.
Armando Guarnaschelli
In this work, a stochastic optimization model is introduced to create Annual Delivery Programs (ADPs) for Liquefied Natural Gas (LNG) supply chains. Every year, liquefaction plants create ADPs to efficiently supply their customers under longmedium and shortterm contracts. This activity has taken great relevance since the SPOT market boom, in which both suppliers and clients may trade during the Gasyear. Spot sourcing and sales take place when supply chain partners look for more profits or need to stabilize variabilities in demand and raw gas supply. Moreover, the high cost of transportation and limited availability of specialized ships to carry it out, call for creating optimal delivery programs that maximize the value functions of both liquefaction plants and their customers. In this context, this proposal relies on stochastic programming to provide an optimized and reliable strategy for ADP creation. The stochastic programming model proves to be hard to solve. To overcome this weakness, a scenario reduction technique based on clustering is provided together with a specialized rolling horizon heuristic. Under this setting, an optimized ADP can be obtained in acceptable computing times. The biobjective nature of this problem is tackled using goal programming on every step of the solution procedure. A discussion on the results of applying this approach to a realworld scenario is included.

On Monotone Nonexpansive Mapping and Their Approximation Fixed Point Results
Buthinah Bin Dehaish
abstract
On Monotone Nonexpansive Mapping and Their Approximation Fixed Point Results
Buthinah Bin Dehaish
Suppose that C is a nonempty closed bounded and convex subset of a metric space X. Let T be a monotone nonexpansive mapping on C. During this talk we will present some existence fixed point result of this mapping. Furthermore, we will describe the behavior of its fixed point by using some constructive iteration.

Kinetic Parameter Identification Based on Spectroscopic Data  advancements Illustrated by Case Studies
Christina Schenk
abstract
Kinetic Parameter Identification Based on Spectroscopic Data  advancements Illustrated by Case Studies
Christina Schenk
The development of drug manufacturing processes involves dealing with spectroscopic data. When dealing with
spectroscopic data, the identification of parameters and variances still remains a challenging task. In many cases
kinetic parameter identification from spectroscopic data has to be performed without knowing the absorbing
species in advance, such that they have to be estimated as well. However, kinetic parameter estimation is
important in order to lower production costs, i.e. save measurements and equipment. Furthermore, scaling up
from laboratory to industrial level relies on accurate kinetic parameter values.
That is why, we take a closer look at the development of optimizationbased procedures in order to estimate the
variances of the noise in the system variables and spectral measurements. Then, with the estimated variances
we determine the concentration profiles and kinetic parameters simultaneously using adequate strategies. The
work is based on the approach proposed by [1] using maximum likelihood principles for simultaneous estimation
of reaction kinetics and curve resolution from process and spectral data. For this a new software environment
was developed which is continuously enhanced. These investigations and advancements are presented within
this talk and illustrated by several case studies of pharmaceutical processes.
References
[1] W Chen, LT Biegler, and SG Muñoz. An approach for simultaneous estimation of reaction kinetics and
curve resolution from process and spectral data. Journal of Chemometrics, 30:506–522, 2016.

Optimization over Invariant Sets of Dynamical Systems
Amir Ali Ahmadi
abstract
Optimization over Invariant Sets of Dynamical Systems
Amir Ali Ahmadi
We study the problem of optimizing over invariant sets of dynamical systems, which we refer to as "robusttodynamics optimization" (RDO). An RDO problem is an optimization problem specified by two pieces of input: (i) a mathematical program (an objective function $f : R^n \to R$ and a feasible
set $\Omega \subseteq R^n$), and (ii) a dynamical system (a map $g : R^n \to R^n$). Its goal is to minimize f over the set $S \subseteq \Omega $ of initial conditions that forever remain in $\Omega$ under $g$. The focus of this talk is on the case where the mathematical program is a linear program and the dynamical system
is either a known linear map, or an uncertain linear map that can change over time. In both cases, we study a converging sequence of polyhedral outer approximations and (lifted) spectrahedral inner approximations to $S$. Our inner approximations are optimized with respect to the objective
function f and their semidefinite characterization—which has a semidefinite constraint of fixed size—is obtained by applying polar duality to convex sets that are invariant under (multiple) linear maps. We characterize three barriers that can stop convergence of the outer approximations to $S$ from being finite. We prove that once these barriers are removed, our inner and outer approximating procedures find an optimal solution and a certificate of optimality for the RDO problem in a finite number of steps. Moreover, in the case where the dynamics are linear, we show that this phenomenon occurs in a number of steps that can be computed in time polynomial in the bit size of the input data. Our analysis also leads to a polynomialtime algorithm for RDO instances where the spectral radius of the linear map is bounded above by any constant less than one. Joint work with Oktay Gunluk.

Distribution Systems Hardening against Natural Disasters
Yushi Tan
abstract
Distribution Systems Hardening against Natural Disasters
Yushi Tan
Distribution systems are often crippled by catastrophic damage caused by natural disasters. Welldesigned hardening can significantly speedup the postdisaster restoration process. This performance is quantified by a resilience measure associated with the operability trajectory. The distribution system hardening problem can be formulated as a twostage stochastic problem, where the inner operational problem addresses the proper scheduling of postdisaster repairs and the outer problem the judicious selection of components to harden. We propose a deterministic single crew approximation with two solution methods, an MILP formulation and a heuristic approach. We provide computational evidence based on several IEEE test feeders, which demonstrates that the heuristic approach provides nearoptimal hardening solutions in a computationall efficient manner.

Tropical Optimization Problems: Recent Results and Applications Examples
Nikolai Krivulin
abstract
Tropical Optimization Problems: Recent Results and Applications Examples
Nikolai Krivulin
We consider multidimensional optimization problems formulated in the tropical mathematics setting to minimize or maximize functions defined on vectors over idempotent semifields, subject to linear equality and inequality constraints. We start with a brief overview of known tropical optimization problems and solution approaches. Furthermore, some new problems are presented with nonlinear objective functions calculated using multiplicative conjugate transposition of vectors, including problems of Chebyshev approximation, problems of approximation in the Hilbert seminorm, and pseudoquadratic problems. To solve these problems, we apply methods based on the reduction to the solution of parametrized inequalities, matrix sparsification, and other techniques. The methods offer direct solutions represented in a compact explicit vector form ready for further analysis and straightforward computation. We conclude with a short discussion of the application of the results obtained to practical problems in location analysis, project scheduling and decision making.

A Further Study on the Opioid Epidemic Dynamical Model with Random Perturbation
Getachew Befekadu
abstract
A Further Study on the Opioid Epidemic Dynamical Model with Random Perturbation
Getachew Befekadu
In this talk, we consider an opioid epidemic dynamical model with random perturbation that describes the interplay between regular prescription use, addictive use, and the process of rehabilitation from addiction and viceversa. In particular, we provide twosided bounds on the solution of the density function for the FokkerPlanck equation that corresponds to the opioid epidemic dynamical model, when the random perturbation enters only through the dynamics of the susceptible group in the compartmental model. Here, the proof for such twosided bounds basically relies on the interpretation of the solution for the density function as the value function of a certain optimal stochastic control problem. Finally, as a possible interesting development in this direction, we also provide an estimate for the attainable exit probability with which the solution for the randomly perturbed opioid epidemic dynamical model exits from a given bounded open domain during a certain time interval.

Motion Planning for Autonomous Vehicles Using MINLP
Hande Benson
abstract
Motion Planning for Autonomous Vehicles Using MINLP
Hande Benson
We will present a mixedinteger nonlinear programming model, its centralized and decentralized solution, for motion planning in fleets of autonomous vehicles (land, water, and aerial) under communication constraints. We will show that a customized approach is necessary for realtime solutions.

Convergence Rate of Stochastic Mirror Descent for Nonsmooth Nonconvex Optimization
Siqi Zhang
abstract
Convergence Rate of Stochastic Mirror Descent for Nonsmooth Nonconvex Optimization
Siqi Zhang
We study the nonasymptotic stationary convergence behavior of Stochastic Mirror Descent (SMD) for a general class of nonconvex nonsmooth stochastic optimization problems, in which the objective can be decomposed into a relatively weakly convex function (possibly nonLipschitz) and a simple nonsmooth convex regularizer. We prove that SMD, without the use of minibatch, is guaranteed to converge to a stationary point in a convergence rate of $ \mathcal{O}(1/\sqrt{t}) $. The efficiency estimate matches with existing results for stochastic subgradient method, but is evaluated under a stronger stationarity measure. This appears to be the first nonasymptotic convergence analysis of SMD for solving relatively weakly convex problems.

Applying the Fractional Natural Decomposition Method to Solve Fractional Differential Equations in Multidimensional Space
Mahmoud Rawashdeh
abstract
Applying the Fractional Natural Decomposition Method to Solve Fractional Differential Equations in Multidimensional Space
Mahmoud Rawashdeh
In recent years, interest in the fractional differential equations has been stimulated due to their wide applications in various fields of engineering and science. Various vital phenomena in electromagnetic, viscoelasticity, fluid mechanics, electrochemistry, biological population models, and signal processing are well described by fractional differential equations. Also, they are employed in social sciences such as food supplement, climate, finance, and economics. As a result, the importance of obtaining exact or approximate solutions of fractional linear and nonlinear differential equations in physics and applied mathematics is still a significant problem that
needs new methods.
We propose a new method called the inverse fractional natural transform method (IFNTM). We present theoretical results and apply them to obtain approximate solutions of linear fractional ordinary differential equations (LFODEs) and partial differential equations (LFPDEs). The fractional derivatives are described in the Caputo sense. The algorithm described in this study is expected to be further
employed to solve similar linear problems in fractional calculus.

Dynamic Appointment Scheduling Problem with Patient Preferences
Secil Sozuer
abstract
Dynamic Appointment Scheduling Problem with Patient Preferences
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 choice. In the first part of the study, we consider that the stochasticity is coming from only uncertain patient arrivals and uncertain service duration realizations. 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. Various sampling methods such as stratified sampling, weighted sampling, and pure random sampling are analyzed within SA algorithm. 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.
In the second part of the study, in addition to having uncertain patient arrivals and uncertain duration realizations, we also take patient choices into account. We consider an appointment system where the patients have preferences about the two appointment days. In order to simulate choice probabilities, we use discrete choice models. We investigate different scheduling policies and conduct empirical analysis by considering the tradeoff between the expected cost and patient satisfaction.


11:45 
12:00 
Coffee break

12:00 
13:00 
Plenary talk
Variabilityaware power operations
Dan Bienstock
abstract
Variabilityaware power operations
Dan Bienstock
Power systems subject to uncertainty increasingly pose a challenge to safe and economical operation. A popular approach to dealing with uncertainty has been to rephrase standard problems so as to incorporate safety constraints, which are frequently stated, for example, as chance constraints, or modeled through scenario generation. In other words one obtains an optimization problem with constraints that guarantee high probability of safety. However, it has also been recognized that variability itself is a hazard, and that operating solutions that are nominally 'safe' may (undesirably) concentrate variability on inappropriate system components (for example, transformers and batteries). This point of view leads to the formulation of optimization problems that blend performance, safety and variability control, and we will discuss several examples. A challenge that is brought about by this approach is how to go about modeling variability. Ideally, we would refer to some type of realtime variance approach. Here we will discuss attributes of actual sensor data obtained through an industrial collaboration, in particular focusing on data features that do not readily fit theoretical models. If time permits we will outline a different application, dealing with counteracting data and physical attacks against transmission systems. Joint work with Apurv Shukla, Mauro Escobar and Michael Chertkov


13:00 
14:00 
Lunch

14:00 
15:30 
Parallel technical sessions
Optimization in Energy

Methods for Nonlinear Optimization

Recent Progress in Stochastic/Robust Optimization and Applications

Derivative Free and BlackBox Optimization

Phase Transitions for Optimality Gaps in Optimal Power Flows
Pascal Van Hentenryck
abstract
Phase Transitions for Optimality Gaps in Optimal Power Flows
Pascal Van Hentenryck
This paper investigates phase transitions on the optimality gaps in Optimal Power Flow (OPF) problem on realworld power transmission systems operated in France. The experimental results study optimal power flow solutions for more than 6000 scenarios on the networks with various load profiles, voltage feasibility regions, generation capabilities and objective functions. The results show that bifurcations between primal solutions and the QC, SOCP, and SDP relaxation techniques frequently occur when approaching congestion points. Moreover, the results demonstrate the existence of multiple bifurcations for certain scenarios when load demands are increased uniformly. Preliminary analysis on these bifurcations were performed.

A Feasible Levelset Method for Optimization with Stochastic or Datadriven Constraints
Qihang Lin
abstract
A Feasible Levelset Method for Optimization with Stochastic or Datadriven Constraints
Qihang Lin
We consider the constrained optimization where the objective function and the constraints are given as either finite sums or expectations. We propose a new feasible levelset method to solve this class of problems, which can produce a feasible solution path. To update a level parameter towards the optimality, our levelset method requires an oracle that generates upper and lower bounds as well as an affineminorant of the level function. To construct the desired oracle, we reformulate the level function as the value of a saddlepoint problem using the conjugate and perspective of constraints. Then a stochastic gradient method with a special Bregman divergence is proposed as the oracle for solving that saddlepoint problem. The special divergence ensures the proximal mapping in each iteration can be solved in a closed form. The total complexity of both levelset methods using the proposed oracle are analyzed.

A Copositive Approach for Multistage Robust Optimization Problems
Grani A. Hanasusanto
abstract
A Copositive Approach for Multistage Robust Optimization Problems
Grani A. Hanasusanto
In this talk, we study generic multistage linear robust optimization problems. We employ linear decision rules for the case when the objective coefficients, the recourse matrices, and the righthand sides are uncertain, and utilize quadratic decision rules for the case when only the righthand sides are uncertain. The emerging optimization problems are NPhard but amenable to copositive programming reformulations that give rise to tight conservative approximations. We provide theoretical and numerical results to demonstrate the effectiveness of the copositive programming approach.

Efficient Optimal Design of Latent Energy Storage Systems
Chunjian Pan
abstract
Efficient Optimal Design of Latent Energy Storage Systems
Chunjian Pan
Due to the intermittent nature of renewable energy resources, latent thermal energy storage (LTES) systems can play an important role in matching supply with demand. Efficient approaches for the optimal design of LTES systems is of particular interest. LTES systems exhibit both nonlinear and transient behaviors. It is computationally expensive to simulate LTES systems, and thus also typically to optimize their design. LTES design optimizations are often based on parametric studies, which neglect the interaction between design variables in this complex system, resulting in unrealistic performance enhancements. In this work, in order to facilitate efficient mathematical optimizations of LTES systems, a combined datadriven and physical knowledgebased model is built. This modeling approach is validated for two LTES systems and integrated into an optimal design framework.

Statistical Learning for (Power System) Optimization: An Active Set Approach
Line Roald
abstract
Statistical Learning for (Power System) Optimization: An Active Set Approach
Line Roald
Many engineering applications such as power system optimization involve solving similar optimization problems over and over and over again, with only slightly varying input parameters. In this talk, we consider the problem of using information available through this repeated solution process to directly learn the optimal solution as a function of the input parameters, thus reducing the need of solving computationally expensive optimization problems in real time.
To overcome limitations of traditional machine learning methods, which often struggle to enforce feasibility constraints or to leverage the knowledge available in the mathematical model, we propose a learning framework based on identifying the relevant set of active constraints (the socalled active set). Using active sets as features enables efficient recovery of the optimal solution, inherently accounts for relevant safety constraints and provides more interpretable results. Further, the number of relevant active sets is finite and sometimes small, which make them simpler objects to learn. To identify the relevant active sets, we propose a streaming algorithm with rigorous probabilistic performance guarantees. The algorithm is demonstrated using the optimal power flow (OPF) problem with renewable energy as an example. We establish that the number of active sets is indeed typically small for this application, and discuss theoretical and practical implications for power systems operation.

Levelset Methods for Finitesum Constrained Convex Optimization
Runchao Ma
abstract
Levelset Methods for Finitesum Constrained Convex Optimization
Runchao Ma
We consider the constrained optimization where the objective function and the constraints are defined as summation of finitely many loss functions. This model has applications in machine learning such as NeymanPearson classification. We consider two levelset methods to solve this class of problems, an existing inexact Newton method and a new feasible levelset method. To update the level parameter towards the optimality, both methods require an oracle that generates upper and lower bounds as well as an affineminorant of the level function. To construct the desired oracle, we reformulate the level function as the value of a saddlepoint problem using the conjugate and perspective of the loss functions. Then a stochastic variancereduced gradient method with a special Bregman divergence is proposed as the oracle for solving that saddlepoint problem. The special divergence ensures the proximal mapping in each iteration can be solved in a closed form. The total complexity of both levelset methods using the proposed oracle are analyzed.

Nurse Staffing under Uncertain Demand and Absenteeism
Minseok Ryu
abstract
Nurse Staffing under Uncertain Demand and Absenteeism
Minseok Ryu
This paper describes a datadriven approach for nurse staffing decision under uncertain demand and absenteeism. We propose a distributionally robust nurse staffing (DRNS) model with both exogenous (stemming from demand uncertainty) and endogenous uncertainty (stemming from nurse absenteeism). We provide a separation approach to solve the DRNS model with general nurse pool structures. Also, we identify several classes of nurse pool structures that often arise in practice and show how the DRNS model in each of these structures can be reformulated as a monolithic mixedinteger linear program that facilitates offtheshelf commercial software. Built upon the DRNS model, furthermore, we propose an optimal nurse pool design model, which produces an optimal pool structure that minimizes the number of crosstraining while achieving a target staffing cost.

A New local Parallelization for Particle Swarm Optimization
Abd AlRahman R. AlMomani Ahmad Almomani
abstract
A New local Parallelization for Particle Swarm Optimization
Abd AlRahman R. AlMomani Ahmad Almomani
Abd AlRahman Al Momani*, Ahmad Almomani**,
*Department of Electrical and Computer Engineering,
Clarkson University, Potsdam, NY, 13699
almomaa@clarkson.edu
**Department of Mathematics,
SUNY Geneseo, Geneseo, NY, 14454
almomani@geneseo.edu
Abstract
Derivativefree methods are highly demanded in the last two decades for solving optimization problems. DerivativeFree Optimization (DFO) are applicable for these problems where the derivatives are not available or hard to compute. Particle Swarm Optimization (PSO) considered one of the best DFO global solvers and had shown to be efficient, few parameters, and flexible optimization algorithm. But it suffers from slow convergence in the refined search stage (weak local searchability), even though PSO resists being trapped in a local optimum but sometimes does. In this talk, an Unsupervised Particle Swarm Optimization (UPSO) algorithm introduced that profoundly improve the reliability, cost, and robustness of PSO. Our approach introduces new position and velocity update strategy based on the weighted gravitational force between all swarm individuals. NelderMead algorithm parallelized with UPSO and Numerical results proposed for most known standard benchmark problems.

From Power System State Estimation to Low Rank Tensor Completion
Cédric Josz
abstract
From Power System State Estimation to Low Rank Tensor Completion
Cédric Josz
A recent line of research in mathematical programming consists of proving that simple and practical algorithms can solve nonconvex optimization problems. This has been of particular interest for machine learning applications, among others; a recent paper by Zhang et al. (https://www.ocf.berkeley.edu/~ryz/pdf/SE\_2018\_1.pdf)discusses the existence of spurious local minima in the context of power system state estimation  which can be viewed as a special case of matrix sensing. This paper finds that as the number of measurements increases, local search algorithms are less likely to get stuck at a spurious local minima. In particular, the GaussNewton algorithm for solving nonlinear least squares generally finds the global minimizer. We consider replacing the least squares objective (i.e. L2 norm) with the L1 norm with the aim of better coping with outliers in the data. This leads us to develop new mathematical tools to handle nonconvex nondifferentiable optimization problems. These apply to state estimation and more generally tensor completion.

An Inexact Penalty Sequential Linear Optimization Method for Constrained Nonlinear Optimization
Yuyang Rong
abstract
An Inexact Penalty Sequential Linear Optimization Method for Constrained Nonlinear Optimization
Yuyang Rong
The primary focus of this paper is on designing inexact penalty sequential linear optimization (commonly known as SLP) methods for solving largescale constrained nonlinear optimization problems. By controlling the inexactness of the linear optimization subproblem solution, we can significantly reduce the computational cost needed per each subproblem. A penalty parameter updating strategy during the subproblem solve enables the algorithm to automatically detect infeasibility. Global convergence for both feasible and infeasible cases are proved. Complexity analysis for the KKT residual is also derived under loose assumptions. Numerical experiments exhibit the ability of the proposed algorithm to find optimal solution through cheap computational cost.

A Datadriven Distributionally Robust Optimization Approach for Appointment Scheduling With Random Service Durations and Noshows
Guanglin Xu
abstract
A Datadriven Distributionally Robust Optimization Approach for Appointment Scheduling With Random Service Durations and Noshows
Guanglin Xu
We study a singleserver appointmentscheduling problem where the number of appointees and the sequence of their arrivals are fixed, and the appointees have noshow behavior. The service durations and noshows are stochastic, but the underlying true probability distribution is un known. With a collection of historical observations, we develop an ambiguity set, which contains the true distribution with a predetermined statistical confidence level. We then develop a dis tributioanlly robust optimization model, which minimizes the worstcase total expected cost of appointment waiting, server idleness, and server overtime, by optimizing the scheduled arrival times of the appointees. Under some mild conditions, we reformulate the resulting problem into a tractable convex program, and for the general case, we propose a copositive program ming reformulation, which motivates a tight semidefiniteprogrammingbased approximation. We validate the effectiveness of our approach on benchmark scheduling instances in the existing literature.

Derivativefree Optimization of Noisy Functions via QuasiNewton Methods
Albert Berahas
abstract
Derivativefree Optimization of Noisy Functions via QuasiNewton Methods
Albert Berahas
We present a finite difference quasiNewton method for the minimization of noisy functions. The method takes advantage of the scalability and power of BFGS updating, and employs an adaptive procedure for choosing the differencing interval at every iteration, based on an estimate of the noise. The noise estimation procedure is inexpensive but not always accurate, and to prevent failures the algorithm incorporates a recovery mechanism that takes appropriate action in the case when the line search procedure is unable to produce an acceptable point. A novel convergence analysis is presented that considers the effect of a (noisy) line search routine. We report results of numerical experiments comparing the method to a popular model based trust region method.

Optimal Power Flow with Robust Feasibility Guarantees
Daniel Molzahn
abstract
Optimal Power Flow with Robust Feasibility Guarantees
Daniel Molzahn
Solutions to optimal power flow (OPF) problems provide minimum cost operating points that satisfy both engineering limits and the power flow equations corresponding to the network physics. To account for the forecast uncertainty and shortterm fluctuations that are inherent to many renewable energy sources, this presentation describes a recently proposed iterative algorithm for OPF problems which provides operating points that are guaranteed to be robust to renewable fluctuations within specified ranges. The algorithm is based on the observation that considering uncertainty leads to a tightening of the original, deterministic constraints in order to safely accommodate fluctuations due to uncertain generation. The main challenge in solving the robust AC OPF problem is to guarantee the existence of feasible solutions for all points within the uncertainty set. To overcome this challenge, the proposed algorithm (1) employs convex relaxations of the AC power flow equations to obtain a conservative estimate of the required tightenings and (2) uses a sufficient condition that ensures power flow solvability for all uncertainty realizations.





15:30 
16:00 
Coffee break

16:00 
17:30 
Parallel technical sessions
Learning and Energy

Nonlinear Optimization

Stochastic and Robust Optimization Algorithms and Applications

Reinforcement Learning for Supply Chain

Data Recovery and Event Identification from Highly Quantized Measurements
Meng Wang
abstract
Data Recovery and Event Identification from Highly Quantized Measurements
Meng Wang
We propose to add noise and apply quantization to synchrophasor measurements to increase the data privacy and reduce the communication cost. This talk focuses on data recovery and event identification at the operators’ side from the highly quantized measurements. Event identification can be achieved by solving a data clustering problem that aims to group measurements affected by the same event together. The recovery and clustering are achieved simultaneously by solving a nonconvex constrained maximum likelihood problem. A fast algorithm with the performance guarantee is proposed to solve the nonconvex problem. The proposed method is evaluated numerically on recorded synchrophasor datasets. With large amounts of measurements, even if the resolution is low, our developed clustering method performs comparably to those methods on highresolution measurements. Thus, the operator can successfully extract information, while an eavesdropper with a limited number of measurement cannot extract useful information even using the same method as the operator.

Revisiting the Foundations of Randomized Gossip Algorithms
Nicolas Loizou
abstract
Revisiting the Foundations of Randomized Gossip Algorithms
Nicolas Loizou
In this work we present a new framework for the analysis and design of randomized gossip algorithms for solving the average consensus problem. We present how randomized Kaczmarztype methods  classical methods for solving linear systems  work as gossip algorithms when applied to a special system encoding the underlying network and explain their distributed nature. We reveal a hidden duality of randomized gossip algorithms, with the dual iterative process maintaining a set of numbers attached to the edges as opposed to nodes of the network. Subsequently, using the new framework we propose novel block and accelerated randomized gossip protocols.

SUNlayer: Stable Denoising with Generative Networks
Soledad Villar
abstract
SUNlayer: Stable Denoising with Generative Networks
Soledad Villar
It has been experimentally established that deep neural networks can be used to produce good generative models for real world data. It has also been established that such generative models can be exploited to solve classical inverse problems like compressed sensing and super resolution. In this work we focus on the classical signal processing problem of image denoising. We propose a theoretical setting that uses spherical harmonics to identify what mathematical properties of the activation functions will allow signal denoising with local methods.

Concise Fuzzy Representation of Big Graphs: A Dimensionality Reduction Approach
Faisal AbuKhzam
abstract
Concise Fuzzy Representation of Big Graphs: A Dimensionality Reduction Approach
Faisal AbuKhzam
The enormous amount of data to be represented using large graphs exceeds in some cases the resources of a conventional computer. Edges in particular can take up a considerable amount of memory as compared to the number of nodes. However, rigorous edge storage might not always be essential to be able to draw the needed conclusions. A similar problem takes records with many variables and attempts to extract the most discernible features. It is said that the "dimension" of this data is reduced. Following an approach with the same objective in mind, we map a graph representation to a kdimensional space and answer queries of neighboring nodes by measuring Euclidean distances. The accuracy of our answers would decrease but would be compensated for by fuzzy logic which gives an idea about the likelihood of error. This method allows for reasonable representation in memory while maintaining a fair amount of useful information. Promising preliminary results are obtained and reported by testing the proposed approach on a number of Facebook graphs.

Renewable Scenario Generation Using Adversarial Networks
Baosen Zhang
abstract
Renewable Scenario Generation Using Adversarial Networks
Baosen Zhang
Scenario generation is an important step in the operation and planning of power systems. In this talk, we present a datadriven approach for scenario generation using the popular generative adversarial networks, where to deep neural networks are used in tandem. Compared with existing methods that are often hard to scale or sample from, our method is easy to train, robust, and captures both spatial and temporal patterns in renewable generation. In addition, we show that different conditional information can be embedded in the framework. Because of the feedforward nature of the neural networks, scenarios can be generated extremely efficiently.

Convergence Rates of Proximal Gradient Methods via the Convex Conjugate
David Gutman
abstract
Convergence Rates of Proximal Gradient Methods via the Convex Conjugate
David Gutman
In this talk we propose a novel proof of the $O(1/k)$ and $O(1/k^2)$ convergence rates of the proximal gradient and accelerated proximal gradient methods for composite convex minimization. The crux of the new proof is an upper bound constructed via the convex conjugate of the objective function.

Stochastic ADMM Frameworks for Resolving Structured Stochastic Convex Programs
Yue Xie
abstract
Stochastic ADMM Frameworks for Resolving Structured Stochastic Convex Programs
Yue Xie
We consider the program: $\min\{ E[f(x,\xi)] + E[g(y,\xi)]  Ax + By = b\}$, which finds application in regularized expected risk minimization and distributed regression. To exploit problem structure and allow for distributed computation, we propose a stochastic inexact ADMM (SIADMM) where subproblems are solved inexactly via stochastic approximation. A.s. convergence and geometric convergence rate of meansquared error can be obtained for SIADMM. Meanwhile, the related program $\min\{E[f(x,\xi)] + g(y)  Ax + By = b\}$ where $g(y)$ is deterministic but nonsmooth is also studied. We propose variable samplesize stochastic ADMM (VSSADMM) and its accelerated variant (AVSSADMM). It is shown that the gap of convergence rate is closed between these stochastic frameworks and their deterministic counterparts. Furthermore, VSSADMM may recover the canonical oracle complexity. Preliminary numerical experiments demonstrate some favorable properties of SIADMM and we observe that AVSSADMM is comparable to the stateofart algorithm in addressing graphguided fused Lasso.

RL for Inventory Optimization: Case on Beer Game
Afshin Oroojlooy
abstract
RL for Inventory Optimization: Case on Beer Game
Afshin Oroojlooy
The beer game is a widely used inclass game that is played in supply chain management classes to demonstrate the bullwhip effect. The game is a decentralized, multiagent, cooperative problem that can be modeled as a serial supply chain network in which agents cooperatively attempt to minimize the total cost of the network even though each agent can only observe its own local information.
Each agent chooses order quantities to replenish its stock. Under some conditions, a basestock replenishment policy is known to be optimal. However, in a decentralized supply chain in which some agents (stages) may act irrationally (as they do in the beer game), there is no known optimal policy for an agent wishing to act optimally.
We propose a machine learning algorithm, based on deep Qnetworks, to optimize the replenishment decisions at a given stage. When playing alongside agents who follow a basestock policy, our algorithm
obtains nearoptimal order quantities. It performs much better than a basestock policy when the other agents use a more realistic model of human ordering behavior. Unlike most other algorithms in the literature, our algorithm does not have any limits on the beer game parameter values. Like any deep learning algorithm, training the algorithm can be computationally intensive, but this can be performed ahead of time; the algorithm executes in real time when the game is played. Moreover, we propose a transfer learning approach so that the training performed for one agent and one set of cost coefficients can be adapted quickly for other agents and costs. Our algorithm can be extended to other decentralized multiagent cooperative games with partially observed information, which is a common type of situation in realworld supply chain problems.

Learning Power Flows with Support Vector Machines
Ram Rajagopal
abstract
Learning Power Flows with Support Vector Machines
Ram Rajagopal
Optimization and management of distribution networks traditionally requires representing the physical laws that relate the power state variables in the system. Typically this requires either prior knowledge or learning the network topology and parameters from timeseries measurements collected across the system. Yet, in realworld systems there are significant uncertainties such as the presence of equipment with unknown control rules that prevent full representation of system physics. Instead, we propose utilizing machine learning to identify the relationships between measurements. We show that a specific choice of kernel support vector machines recovers the power flow equations correctly although in a different representation. The approach can correctly learn relationships even in the presence of significant unmodelled components. We conclude the talk demonstrating how machine learning can be utilized to perform a basic reactive power optimization task in the network utilizing an efficient algorithm.

Efficient Distributed Hessian Free Algorithm for Largescale Empirical Risk Minimization via Accumulating Sample Strategy
Majid Jahani
abstract
Efficient Distributed Hessian Free Algorithm for Largescale Empirical Risk Minimization via Accumulating Sample Strategy
Majid Jahani
In this paper, we propose a Distributed Accumulated Newton Conjugate gradiEnt (DANCE) method in which sample size is gradually increasing to quickly obtain a solution whose empirical loss is under satisfactory statistical accuracy. Our proposed method is multistage in which the solution of a stage serves as a warm start for the next stage which contains more samples (including the samples in the previous stage). The proposed multistage algorithm reduces the number of passes over data to achieve the statistical accuracy of the full training set. Moreover, our algorithm in nature is easy to be distributed and shares the strong scaling property indicating that acceleration is always expected by using more computing nodes. Various iteration complexity results regarding descent direction computation, communication efficiency and stopping criteria are analyzed under convex setting. Our numerical results illustrate that the proposed algorithm can outperform other comparable methods for training machine learning tasks including neural networks.

Exploiting Problem Structure in Optimization under Uncertainty via Online Convex Optimization
Nam HoNguyen
abstract
Exploiting Problem Structure in Optimization under Uncertainty via Online Convex Optimization
Nam HoNguyen
Online convex optimization (OCO) has seen much success for its ability to handle decisionmaking in dynamic, uncertain, and even adversarial environments. In this work, we exploit these favorable attributes of OCO to develop iterative frameworks for two paradigms in optimization under uncertainty. First, we consider the generic robust convex optimization (RCO) paradigm seeking solutions that are robust to worstcase noise e.g., data perturbations from a fixed uncertainty set. By reformulating this problem as a convexnonconcave saddle point problem, we avoid relying on robust counterparts, and instead exploit OCO to solve it using only simple firstorder updates. Second, we demonstrate how OCO can be utilized within the joint estimationoptimization (JEO) paradigm, where the data associated with the optimization problem are continuously updated via an estimation process during the optimization procedure. We illustrate our results for the JEO paradigm on the problem of dynamic estimation of nonparametric choice models from continuously collected observational data.

Reinforcement Learning for Solving the Vehicle Routing Problem
MohammadReza Nazari
abstract
Reinforcement Learning for Solving the Vehicle Routing Problem
MohammadReza Nazari
We present an endtoend framework for solving the Vehicle Routing Problem (VRP) using reinforcement learning. In this approach, we train a single model that finds nearoptimal solutions for problem instances sampled from a given distribution, only by observing the reward signals and following feasibility rules. Our model represents a parameterized stochastic policy, and by applying a policy gradient algorithm to optimize its parameters, the trained model produces the solution as a sequence of consecutive actions in real time, without the need to retrain for every new problem instance. On capacitated VRP, our approach outperforms classical heuristics and Google's ORTools on mediumsized instances in solution quality with comparable computation time (after training). We demonstrate how our approach can handle problems with split delivery and explore the effect of such deliveries on the solution quality. Our proposed framework can be applied to other variants of the VRP such as the stochastic VRP, and has the potential to be applied more generally to combinatorial optimization problems.

Learning and Control in Distribution Grids
Michael Chertkov
abstract
Learning and Control in Distribution Grids
Michael Chertkov
Distribution Networks provide the final tier in the transfer of electricity from generators to the end consumers. In recent years, smart controllable devices, residential generator/storage devices and distribution grid meters have expanded the availability of sensor data in distribution networks. We discuss learning and control problems in distribution grid using available timeseries measurements. For a range of realistic operating conditions, machine learning algorithms based on the dynamics of power flows are proposed to learn the structure of the distribution network as well as to estimate the statistics of load profiles at missing nodes and/or line parameters. The learning methods are generalizable for estimation of in other network of interest like sensor networks and smart buildings. We also discuss a Markov Decision Process framework for network aware control of smart devices in distribution grids under uncertainty that cooptimizes user comfort and global objectives.





19:00 
21:00 
Graduate Student Social  Packer House, 217 West Packer Avenue, Bethlehem
