Math 4620/5620: Linear and nonlinear optimization

Handouts

Introduction

Chapter on Introduction to Linear Programming

Applications of Linear Programming 1 Partial Solutions

Applications of Linear Programming 2 Partial Solutions

Applications of Linear Programming 3 Partial Solutions

Chapter on Simplex Method

Simplex handout 1 (Important concepts/definitions; graphical solution of LPs; classification of LPs)

Simplex handout 2 (Towards the simplex method; structure of simplex; definition of basic solutions)

Simplex handout 3 (Details of simplex method)

Simplex handout 4 (Tableau method; two-phase method)

Simplex handout 5 (Solving unbounded problems; multiple optimal solutions; breaking ties; degeneracy)

Beale's example on cycling

Solving Integer Programs (optional)

Solving network problems by integer programming (optional)

Application of Linear Programming in Electoral Systems

Chapter on Theory of Simplex Method

Revised Simplex

Fundamental Insight

Chapter on Duality Theory and Sensitivity Analysis

Sensitivity Analysis I

Duality Theory I

Duality Theory II

Duality Theory III

Sensitivity Analysis II

Sensitivity Analysis III(optional)

Chapter on Network Optimization Models

Network Models I

Network Models II

Network Simplex

Phase 1 and Sensitivity Analysis for Network Simplex

Chapter on Game Theory

Game Theory

Chapter on Nonlinear Programming

Nonlinear Programming I

Nonlinear Programming II

Discrete Optimization (optional)

Interior Point Methods (optional)