**LINEAR PROGRAMMING**

**An Introduction to Linear Programming**

The Basic Linear Programming Problem Formulation

Linear Programming: A Graphical Perspective in R^{2}

Basic Feasible Solutions

**The Simplex Algorithm**

The Simplex Algorithm

Alternative Optimal/Unbounded Solutions and Degeneracy

Excess and Artificial Variables: The Big M Method

A Partitioned Matrix View of the Simplex Method

The Revised Simplex Algorithm

Moving beyond the Simplex Method: An Interior Point Algorithm

**Standard Applications of Linear Programming**

The Diet Problem

Transportation and Transshipment Problems

Basic Network Models

**Duality and Sensitivity Analysis**

Duality

Sensitivity Analysis

The Dual Simplex Method

**Integer Linear Programming**

An Introduction to Integer Linear Programming and the Branch and Bound Method

The Cutting Plane Algorithm

**NONLINEAR PROGRAMMING**

**Algebraic Methods for Unconstrained Problems**

Nonlinear Programming: An Overview

Differentiability and a Necessary First-Order Condition

Convexity and a Sufficient First-Order Condition

Sufficient Conditions for Local and Global Optimal Solutions

**Numeric Tools for Unconstrained Nonlinear Problems**

The Steepest Descent Method

Newton’s Method

The Levenberg–Marquardt Algorithm

**Methods for Constrained Nonlinear Problems**

The Lagrangian Function and Lagrange Multipliers

Convex Nonlinear Problems

Saddle Point Criteria

Quadratic Programming

Sequential Quadratic Programming

**Appendix A: Projects**

**Appendix B: Important Results from Linear Algebra**

**Appendix C: Getting Started with Maple**

**Appendix D: Summary of Maple Commands **

**Bibliography **

**Index**