Optimization

Optimization: Algorithms and Applications presents a variety of solution tech-

niques 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 optimiza-

tion problems using simple modications of the basic PSO code. The book also

introduces multidisciplinary design optimization (MDO) architectures—one of the

rst optimization books to do so—and develops software codes for the simplex

method and afne-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 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 de-

sign 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 condence in handling different solution methods.

Features

• Explains how to solve complex optimization problems using gradient-based

and stochastic methods

• Describes different architectures to handle MDO problems

• Solves many practical problems using MATLAB

• Links the software code to the corresponding algorithms in a user-friendly

way

• Provides the MATLAB codes for download on the book’s CRC Press web

page

K25568

www.crcpress.com

OPTIMIZATION

OPTIMIZATION

Algorithms and

Applications

Rajesh Kumar Arora

Arora

Mathematics

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