LINEAR PROGRAMMING
An Introduction to Linear Programming
The Basic Linear Programming Problem Formulation
Linear Programming: A Graphical Perspective in R2
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