Teaching

“Two years!” exclaimed Dantès; “do you really believe I can acquire all these things in so short a time?”

“Not their application, certainly, but their principles you may; to learn is not to know; there are the learners and the learned. Memory makes the one, philosophy the other.”

Alexandre Dumas — The Count of Monte Cristo

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Columbia University

IEOR E6616 Convex Optimization

  • Semester(s):
    • Spring 2018, syllabus (pdf)
  • Topics:
    • Convex Sets
    • Projections, Hulls, and Relative Interiors
    • Recession Cones and Lineality Spaces
    • Hyperplanes, Separation, and Polyhedral Sets
    • Convex Functions
    • Conjugate Functions
    • Fundamentals of Convex Optimization
    • Geometric Duality Framework
    • Convex Optimization Problems
    • Subdifferential Theory
    • First-Order Algorithms
    • Second-Order Algorithms

Lehigh University

ISE 172 Algorithms for Systems Engineering

  • Semester(s):
    • Spring 2011, syllabus (pdf)
  • Topics:
    • Growth of Functions
    • Analyzing Algorithms
    • Recursion
    • Sorting Algorithms
    • Hash Tables
    • Graph Algorithms
    • Network Problems
    • String Matching
    • Cryptography
    • Matrix Operations
    • Systems of Equations

ISE 220 Introduction to Operations Research

  • Semester(s):
    • Fall 2011, syllabus (pdf)
    • Fall 2010, syllabus (pdf)
    • Fall 2009, syllabus (pdf)
  • Topics:
    • Linear Optimization
    • Simplex Method
    • Duality and Sensitivity Analysis
    • Transportation and Assignment Problems
    • Network Models
    • Discrete Optimization
    • Nonlinear Optimization
    • Markov Chains
    • Queueing Theory

ISE 230 Introduction to Stochastic Models in Operations Research

  • Semester(s):
    • Fall 2021, syllabus (pdf)
    • Spring 2021, syllabus (pdf)
  • Topics:
    • Optimization Under Uncertainty
    • Decision Analysis
    • Game Theory
    • Markov Chains
    • Queueing Theory
    • Dynamic Programming
    • Markov Decision Processes

ISE 401 Convex Analysis

(formerly ISE 496 Convex Analysis and Optimization)

  • Semester(s):
    • Fall 2024, syllabus (pdf)
    • Fall 2022, syllabus (pdf)
    • Fall 2021, syllabus (pdf)
    • Fall 2020, syllabus (pdf)
    • Fall 2019, syllabus (pdf)
    • Fall 2018, syllabus (pdf)
    • Fall 2016, syllabus (pdf)
    • Fall 2015, syllabus (pdf)
    • Fall 2014, syllabus (pdf)
    • Spring 2014, syllabus (pdf)
  • Topics:
    • Convex Sets and Functions
    • Characterizing Convexity and Closedness
    • Projections, Hulls, Interiors, and Closures
    • Recession Cones and Functions
    • Hyperplanes and Conjugacy
    • Polyhedral Convexity
    • Convex Optimization
    • Min Common and Max Crossing Duality
    • Weak and Strong Duality
    • Nonlinear Farkas Lemma
    • Subdifferential Calculus
    • Theorems of the Alternative

ISE 402 Applied Models in Operations Research

  • Semester(s):
    • Spring 2020, syllabus (pdf)
  • Topics:
    • Optimization Modeling
    • Multi-objective Optimization
    • Dynamic Programming
    • Markov Decision Processes
    • Inventory Optimization
    • Facility Location
    • Healthcare Systems
    • Power Systems
    • Disaster Relief

ISE 403 Research Methods

  • Semester(s):
    • Fall 2024, syllabus (pdf)
    • Fall 2023, syllabus (pdf)
  • Topics:
    • Computing Skills (Linux, LaTeX, git, make)
    • Mathematical Background (logic, real analysis, linear algebra, probability)
    • Presentation Skills
    • Time Management
    • Technical Writing
    • Research Ethics

ISE 409 Time Series Analysis

  • Semester(s):
    • Spring 2015, syllabus (pdf)
    • Spring 2014, syllabus (pdf)
    • Spring 2013, syllabus (pdf)
    • Fall 2011, syllabus (pdf)
    • Spring 2010, syllabus (pdf)
  • Topics:
    • Classical Decomposition Models
    • Smoothing, Filtering, Fitting, and Differencing
    • Stationarity and Ergodicity
    • White Noise, AR(p), MA(q), and ARMA(p,q) Processes
    • Mean, Autocovariance, and Autocorrelation Functions
    • Bartlett’s Formula
    • Testing for IID Noise
    • Forecasting ARMA Processes
    • Yule-Walker Equations
    • Burg’s, Innovations, and Hannan-Rissanen Algorithms
    • Maximum Likelihood Estimation and the AICC
    • ARIMA Models
    • Multivariate Time Series
    • State-Space Models and the Kalman Recursions
    • Spectral Analysis

ISE 417 Nonlinear Optimization

  • Semester(s):
    • Spring 2019, syllabus (pdf)
    • Spring 2017, syllabus (pdf)
    • Spring 2016, syllabus (pdf)
    • Spring 2015, syllabus (pdf)
    • Fall 2013, syllabus (pdf)
    • Spring 2012, syllabus (pdf)
    • Fall 2010, syllabus (pdf)
  • Topics:
    • Optimality Conditions for Unconstrained Optimization
    • Convex Optimization Algorithms
    • Newton’s Method for Nonlinear Equations
    • Line Search Methods
    • Trust Region Methods
    • Conjugate Direction Methods
    • Quasi-Newton Methods
    • Optimality Conditions for Constrained Optimization
    • Duality and Constraint Qualifications
    • Linear and Quadratic Optimization
    • Penalty Methods
    • Sequential Quadratic Optimization
    • Interior-Point Methods

ISE 496 Numerical Methods for Optimal Control

  • Semester(s):
    • Fall 2012, syllabus (pdf)
  • Topics:
    • Calculus of Variations
    • Euler-Lagrange Equation
    • Hamiltonian Mechanics
    • Pontryagin’s Maximum Principle
    • Numerical Methods for Solving ODEs
    • Calculus of Variations
    • Direct Methods for Solving Optimal Control Problems
    • Sequential Quadratic Optimization
    • Interior-Point Methods
    • Dynamic Optimization
    • Hamilton-Jacobi-Bellman Equation

New York University

Advanced Topics in Numerical Analysis:
Nonlinear Optimization

  • Semester(s):
    • Spring 2008, syllabus (html)
  • Topics:
    • Optimality Conditions for Unconstrained Optimization
    • Line Search Methods
    • Trust Region Methods
    • Conjugate Direction Methods
    • Quasi-Newton Methods
    • Nonlinear Equations and Least-Squares Problems
    • Optimality Conditions for Constrained Optimization
    • Linear and Quadratic Optimization
    • Sequential Quadratic Optimization
    • Interior-Point Methods

Linear Algebra

  • Semester(s):
    • Fall 2008, syllabus (pdf)
  • Topics:
    • Systems of Linear Equations
    • Vector and Matrix Equations
    • Gaussian Elimination
    • Spans, Linear Combinations, and Linear Independence
    • Matrix Inverses and Factorizations
    • Determinants
    • Vector Spaces
    • Null Spaces, Column Spaces, and Bases
    • Eigenvalues, Eigenvectors, and Characteristic Equations
    • Discrete Dynamical Systems
    • Orthogonal Sets and Orthogonal Projections
    • Symmetric Matrices and Quadratic Forms
    • Singular Value Decompositions

Calculus II

  • Semester(s):
    • Spring 2009, syllabus (html)
  • Topics:
    • Definite and Indefinite Integrals
    • Integration by Substitution, Parts, and Partial Fraction Decomposition
    • Distances, Areas, and Volumes
    • Areas between Curves
    • Differential Equations
    • Sequences and Series
    • Power, Taylor, and Maclaurin Series
    • Parametric Curves
    • Polar Coordinates

Quantitative Reasoning: Elementary Statistics

  • Semester(s):
    • Fall 2007, syllabus (pdf)
  • Topics:
    • Nominal, Ordinal, Interval, and Ratio Data Sets
    • Unions and Intersections
    • Permutations and Combinations
    • Means, Medians, and Modes
    • Standard Deviations and Variances
    • Frequency Distributions, Histograms, and Scatterplots
    • Probability of Events
    • Bayes Theorem
    • Mathematical Expectation
    • Probability Distributions
    • Central Limit Theorem
    • Confidence Intervals
    • Hypothesis Testing

Northwestern University

Optimization Methods for Data Science

  • Semester(s):
    • Spring 2018
  • Topics:
    • Optimization Basics
    • Convex Optimization
    • First-Order Methods
    • Nonconvex Optimization
    • Nonsmooth Optimization
    • Second-Order Methods
    • Solving Linear Systems
    • Stochastic Methods
    • Constrained Optimization