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Optimization: Algorithms and Applications

Rajesh Kumar Arora
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2015
Number of Pages: 
450
Format: 
Hardcover
Price: 
129.95
ISBN: 
9781498721127
Category: 
Textbook
[Reviewed by
Underwood Dudley
, on
03/4/2016
]

In his preface, the author writes “So how does this book differ from the others? The solution techniques are detailed in such a way that more emphasis is given to the concepts and rigorous mathematical details and proofs are avoided.”

That means that the techniques are given mostly by examples. The author is an engineer and this is an engineer’s book. As the table of contents shows, many methods are covered, including the conjugate gradient method, the Broyden-Fletcher-Goldfarb-Shanno algorithm, penalty functions, augmented Lagrange multipliers, sequential quadratic programming, feasible directions, particle swram optimization, simulated annealing, and ant colony optimization.

It would be best if a reader of the book is familiar with Matlab. Eighty pages in an appendix are devoted to Matlab code for various algorithms and many of the examples include the output that they provide. Users do not have to retype the code — the algorithms are available at a website.

Each chapter contains exercises, with solutions at the back of the book. Many references are provided.

The book is well produced and is pleasing to the eye. There are a few errors — problem 23 in chapter 1 asks the reader to do something with “the following system of equations” but there are no equations in what follows — but not many. The author or the publisher decided that displayed lines are not parts of the sentences they are in; I think that’s unfortunate but younger readers may not mind (or even notice).

The book will no doubt be useful to those looking for ways to find maxima and minima.

Woody Dudley’s mathematical training lies so far in the past (B. S., 1957) that he had never heard of ant colony optimization, but he admires those who can deal with it.

Introduction
Historical Review
Optimization Problem
Modeling of the Optimization Problem
Solution with the Graphical Method
Convexity
Gradient Vector, Directional Derivative, and Hessian Matrix
Linear and Quadratic Approximations
Organization of the Book

 

1-D Optimization Algorithms
Introduction
Test Problem
Solution Techniques
Comparison of Solution Methods

 

Unconstrained Optimization
Introduction
Unidirectional Search
Test Problem
Solution Techniques
Additional Test Functions
Application to Robotics

 

Linear Programming
Introduction
Solution with the Graphical Method
Standard Form of an LPP
Basic Solution
Simplex Method
Interior-Point Method
Portfolio Optimization

 

Guided Random Search Methods
Introduction
Genetic Algorithms
Simulated Annealing
Particle Swarm Optimization
Other Methods

 

Constrained Optimization
Introduction
Optimality Conditions
Solution Techniques
Augmented Lagrange Multiplier Method
Sequential Quadratic Programming
Method of Feasible Directions
Application to Structural Design

 

Multiobjective Optimization
Introduction
Weighted Sum Approach
ε-Constraints Method
Goal Programming
Utility Function Method
Application

 

Geometric Programming
Introduction
Unconstrained Problem
Dual Problem
Constrained Optimization
Application

 

Multidisciplinary Design Optimization
Introduction
MDO Architecture
MDO Framework
Response Surface Methodology

 

Integer Programming
Introduction
Integer Linear Programming
Integer Nonlinear Programming

 

Dynamic Programming
Introduction
Deterministic Dynamic Programming
Probabilistic Dynamic Programming

 

Bibliography

Appendix A: Introduction to MATLAB
Appendix B: MATLAB Code
Appendix C: Solutions to Chapter Problems

Index

Tags: 
Optimization