Optimization: Algorithms and Applications, 1st Edition (Hardback) book cover

Optimization

Algorithms and Applications, 1st Edition

By Rajesh Kumar Arora

Chapman and Hall/CRC

466 pages | 136 B/W Illus.

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pub: 2015-05-06
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Description

Choose the Correct Solution Method for Your Optimization Problem

Optimization: Algorithms and Applications presents a variety of solution techniques for optimization problems, emphasizing concepts rather than rigorous mathematical details and proofs.

The book covers both gradient and stochastic methods as solution techniques for unconstrained and constrained optimization problems. It discusses the conjugate gradient method, Broyden–Fletcher–Goldfarb–Shanno algorithm, Powell method, penalty function, augmented Lagrange multiplier method, sequential quadratic programming, method of feasible directions, genetic algorithms, particle swarm optimization (PSO), simulated annealing, ant colony optimization, and tabu search methods. The author shows how to solve non-convex multi-objective optimization problems using simple modifications of the basic PSO code. The book also introduces multidisciplinary design optimization (MDO) architectures—one of the first optimization books to do so—and develops software codes for the simplex method and affine-scaling interior point method for solving linear programming problems. In addition, it examines Gomory’s cutting plane method, the branch-and-bound method, and Balas’ algorithm for integer programming problems.

The author follows a step-by-step approach to developing the MATLAB® codes from the algorithms. He then applies the codes to solve both standard functions taken from the literature and real-world applications, including a complex trajectory design problem of a robot, a portfolio optimization problem, and a multi-objective shape optimization problem of a reentry body. This hands-on approach improves your understanding and confidence in handling different solution methods. The MATLAB codes are available on the book’s CRC Press web page.

Table of Contents

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

Chapter Highlights, Formula Charts, and Problems appear at the end of each chapter.

About the Author

Rajesh Kumar Arora is a senior engineer at the Indian Space Research Organization, where he has been working for more than two decades. He obtained his PhD in aerospace engineering from the Indian Institute of Science, Bangalore. His research interests include mission design, simulation of launch vehicle systems, and trajectory optimization.

Subject Categories

BISAC Subject Codes/Headings:
BUS049000
BUSINESS & ECONOMICS / Operations Research
MAT004000
MATHEMATICS / Arithmetic
TEC029000
TECHNOLOGY & ENGINEERING / Operations Research