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Linear and Nonlinear Programming with Maple: An Interactive, Applications-Based Approach

Paul E. Fishback
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2010
Number of Pages: 
391
Format: 
Hardcover
Series: 
Texts in Mathematics
Price: 
89.95
ISBN: 
9781420090642
Category: 
Textbook
[Reviewed by
E. Keith Sinkhorn
, on
03/16/2010
]

In the Foreword to Linear and Nonlinear Programming with Maple™, author Paul E. Fishback states that a primary goal is to provide a text that bridges the gap between management science books that are too light on mathematical rigor and more advanced texts that are written at too high a level for undergraduates. The obvious question is whether or not he is successful in this endeavor. Realistically, the answer to this question depends on what one is looking for in such an undergraduate text.

The book is organized into two parts — five chapters are devoted to linear programming, and three to nonlinear programming. Part I consists of a brief introduction to modeling, the simplex algorithm, integer programming, and applications such as network models, duality theory, and sensitivity analysis. Part II includes algebraic and numeric methods for unconstrained problems as well as a chapter on methods for constrained problems.

It seems peculiar that a text intended for undergraduates focuses almost exclusively on linear and nonlinear programming. A two-semester undergraduate engineering sequence in operations research typically includes a single semester each of deterministic and stochastic (queuing theory, markov chains, etc.) methods. Mathematics programs that offer operations research tend to include a single course reviewing both deterministic and stochastic topics. Unfortunately, the focus of this text is too narrow for either of those cases.

That said, this text could be ideal for the right course and the right group of students. An independent or directed study in mathematical programming using this book could be an excellent introduction to applied optimization for an interested group of undergraduates.

There are a few places where text could be improved. First, the grid-based formatting of simplex tableaux is distracting to the eye, and the fractions do not completely fit within the gridlines. The text would be a more effective, comprehensive package if the accompanying Maple routines were included either in an attached CD-ROM or on a website.


Keith Sinkhorn has a PhD in Industrial Engineering from the University of Louisville. He is an Assistant Professor of Mathematics at Peru State College in Peru, NE with research interests including applied operations research, logistics, discrete optimization, and heuristic algorithms.

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

Dummy View - NOT TO BE DELETED