Linear Programming Duality

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Page 3 of 4

Explores strong duality, complementary slackness, economic interpretation, and stochastic problem scenarios in linear programming.

Introduction to Optimization and Operations Research

Covers fundamental concepts of optimization and operations research, exploring real-world examples and key topics over a semester.

Network Flows and LP Formulations

Explains network flows, LP formulations, simplex method, duality, and practical applications.

Integer Programming Basics

Introduces the basics of integer programming, including binary integer programs and constraint strategies.

Optimization Problems: Path Finding and Portfolio Allocation

Covers optimization problems in path finding and portfolio allocation.

Primal-dual Optimization: Fundamentals

Explores primal-dual optimization, minimax problems, and gradient descent-ascent methods for optimization algorithms.

Linear Programming: Extreme Points

Explores extreme points in linear programming and the role of constraints in finding optimal solutions.

Weak and Strong Duality

Covers weak and strong duality in optimization problems, focusing on Lagrange multipliers and KKT conditions.

Optimality Conditions in Linear Optimization

Covers optimality conditions, strong duality, and complementarity slackness in linear optimization.

Lagrangian Duality: Convex Optimization

Explores Lagrangian duality in convex optimization, transforming problems into min-max formulations and discussing the significance of dual solutions.