Simplex Algorithm: Graphical Method

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Explains the SIMPLEX method for solving linear programs and optimizing the solution through basis variable manipulation.

Optimization Principles

Covers optimization principles, including linear optimization, networks, and concrete research examples in transportation.

Linear Optimization: Auxiliary Problem

Explores the formulation of the auxiliary problem in linear optimization and its role in optimal decision-making.

Discrete Optimization: Relaxation

Explores solving discrete optimization problems by relaxing integrality constraints.

Linear Optimization: Fundamentals

Covers the basics of linear optimization, including equations, polyhedrons, feasible directions, and optimal solutions.

Simplex Algorithm: Solution on a Vertex

Explores the simplex algorithm and how optimal solutions can be found on vertices of constraint polyhedra.

Two-phase Simplex Algorithm: Introduction and Duality

Introduces the two-phase simplex algorithm and explores duality in linear programming.

Simplex Algorithm: Basics

Introduces the Simplex algorithm for solving flow problems and handling negative cost cycles.

Convex Optimization Tutorial: KKT Conditions

Explores KKT conditions in convex optimization, covering dual problems, logarithmic constraints, least squares, matrix functions, and suboptimality of covering ellipsoids.

Introduction to Optimization and Operations Research

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