Practical Methods of Optimization - Hardcover

Fletcher, R.

Hardcover

ISBN 10: 0471915475 ISBN 13: 9780471915478

Publisher: John Wiley & Sons, 1995

Synopsis

Fully describes optimization methods that are currently most valuable in solving real–life problems. Since optimization has applications in almost every branch of science and technology, the text emphasizes their practical aspects in conjunction with the heuristics useful in making them perform more reliably and efficiently. To this end, it presents comparative numerical studies to give readers a feel for possibile applications and to illustrate the problems in assessing evidence. Also provides theoretical background which provides insights into how methods are derived. This edition offers revised coverage of basic theory and standard techniques, with updated discussions of line search methods, Newton and quasi–Newton methods, and conjugate direction methods, as well as a comprehensive treatment of restricted step or trust region methods not commonly found in the literature. Also includes recent developments in hybrid methods for nonlinear least squares; an extended discussion of linear programming, with new methods for stable updating of LU factors; and a completely new section on network programming. Chapters include computer subroutines, worked examples, and study questions.

About this title

From the Back Cover

This established textbook is noted for its coverage of optimization methods that are of practical importance. It provides a thorough treatment of standard methods such as linear and quadratic programming, Newton–like methods and the conjugate gradient method. The theoretical aspects of the subject include an extended treatment of optimality conditions and the significance of Lagrange multipliers. The relevance of convexity theory to optimization is also not neglected. A significant proportion of the book is devoted to the solution of nonlinear problems, with an authoritative treatment of current methodology. Thus state of the art techniques such as the BFGS method, trust region methods and the SQP method are described and analysed. Other features are an extensive treatment of nonsmooth optimization and the L―1 penalty function. Contents Part 1 Unconstrained Optimization Part 2 Constrained Optimization
∗ Introduction
∗ Structure of Methods
∗ Newton–like Methods
∗ Conjugate Direction Methods
∗ Restricted Step Methods
∗ Sums of Squares and Nonlinear Equations
∗ Introduction
∗ Linear Programming
∗ The Theory of Constrained Optimization
∗ Quadratic Programming
∗ General Linearly Constrained Optimization
∗ Nonlinear Programming
∗ Other Optimization Problems

Synopsis

The second edition of this established textbook combines volumes 1 and 2 of the first edition. The presentation and theory in this new edition have been extended and improved, and a number of new developments are described including an extended treatment of linear programming and important recent advances in polynomial time algorithms. There are new sections on network programming, a subject of great practical importance, and on optimality conditions for constrained composite non-smooth optimization. Throughout the book the emphasis is on practicability, and a great deal of attention is given to methods which have proved reliable and efficient. The first edition included frequent worked examples and exercises which both illustrated and extended the text, and these have been augmented in this combined second edition.

Edition details

• Publisher: John Wiley & Sons
• Publication date: 1995
• Language: English
• ISBN 10: 0471915475
• ISBN 13: 9780471915478
• Binding: Hardcover
• Edition number: 2
• Number of pages: 436