Optimization Theory and Methods: Nonlinear Programming / Edition 1

by Wenyu Sun, Ya-Xiang Yuan

Overview

This book, a result of the authors’ teaching and research experience in various universities and institutes over the past ten years, can be used as a textbook for an optimization course for graduates and senior undergraduates. It systematically describes optimization theory and several powerful methods, including recent results. For most methods, the authors discuss an idea’s motivation, study the derivation, establish the global and local convergence, describe algorithmic steps, and discuss the numerical performance. The book deals with both theory and algorithms of optimization concurrently. It also contains an extensive bibliography with 366 references. Finally, apart from its use for teaching, Optimization Theory and Methods is also very beneficial for doing research.

Audience

This book is intended for senior students, graduates, teachers, and researchers in optimization, operations research, computational mathematics, applied mathematics, and some engineering and economics. It will also be useful for scientists in engineering and economics.

Product Details

ISBN-13:	9780387249759
Publisher:	Springer US
Publication date:	05/24/2006
Series:	Springer Optimization and Its Applications , #1
Edition description:	2006
Pages:	687
Product dimensions:	6.14(w) x 9.25(h) x 0.06(d)

Table of Contents

Line Search.- Newton’s Methods.- Conjugate Gradient Method.- Quasi-Newton Methods.- Trust-Region Methods and Conic Model Methods.- Solving Nonlinear Least-Squares Problems.- Theory of Constrained Optimization.- Quadratic Programming.- Penalty Function Methods.- Feasible Direction Methods.- Sequential Quadratic Programming.- Trust-Region Methods for Constrained Problems.- Nonsmooth Optimization.

Editorial Reviews

From the reviews:

"The book contains a comprehensive presentation of methods for unconstrained and constrained optimization problems. … The main strength of the book is the precise convergence analysis of most nonlinear programming algorithms presented, and it is especially comprehensive for line search, Newton, quasi-Newton, trust region and SQP methods. In this respect the book is a very valuable reference." (Darinka Dentcheva, Mathematical Reviews, Issue 2007 c)

"Optimization is a subject that is widely and increasingly used in science, engineering, economics, management, industry, and other areas. … The book is self-contained, systematic in theory and algorithms, and easy to read. … The book also contains an extensive … bibliography with 366 references, which is an important part of the book, and is useful to readers for further studies. Each chapter ends with an exercise set." (Alexandr B. Vasil’ev, Zentralblatt MATH, Vol. 1129 (7), 2008)

From the Publisher