Nonlinear Programming: Theory and Algorithms, Third Edition

基本信息

Format:Hardback 872 pages

Publisher:John Wiley & Sons Inc

Imprint:John Wiley & Sons Inc

Edition:3rd Edition

ISBN:9780471486008

Published:20 Apr 2006

Weight:1294g

Dimensions:167 x 241 x 53 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

经典的非线性规划教材。针对非线性规划问题，提出相应的理论和求解算法。

COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED

Nonlinear Programming: Theory and Algorithms—now in an extensively updated Third Edition—addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The Third Edition begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction.

Concentration on the three major parts of nonlinear programming is provided:

• Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programming

• Optimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditions

• Algorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problems

Important features of the Third Edition include:

• New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and more

• Updated discussion and new applications in each chapter

• Detailed numerical examples and graphical illustrations

• Essential coverage of modeling and formulating nonlinear programs

• Simple numerical problems

• Advanced theoretical exercises

The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems.

NEW TO THIS EDITION

Is updated throughout with new content, including, but not limited to, discussions on second-order necessary conditions, variable target value methods, primal-dual path, and quadratic constraints, among others

Includes over three new applications per chapter to showcase the currency of the content 

FEATURES

Covers, in-depth, a topic which is typically not given much attention

Incorporates timely footnotes and references throughout the text to keep the reader well-informed of changes in the marketplace

Has ample exercises which reinforce the theory and concepts presented in the text

Has been extensively class-tested, over a fifteen-year period, to avoid errata and annoying misconceptions about NLP techniques

目录

Chapter 1 Introduction.

Part 1 Convex Analysis.

Chapter 2 Convex Sets.

Chapter 3 Convex Functions and Generalizations.

Part 2 Optimality Conditions and Duality.

Chapter 4 The Fritz John and Karush-Kuhn-Tucker Optimality Conditions.

Chapter 5 Constraint Qualifications.

Chapter 6 Lagrangian Duality and Saddle Point Optimality Conditions.

Chapter 7 The Concept of an Algorithm.

Chapter 8 Unconstrained Optimization.

Chapter 9 Penalty and Barrier Functions.

Chapter 10 Methods of Feasible Directions.

Chapter 11 Linear Complementary Problem, and Quadratic, Separable, Fractional, and Geometric Programming.

Appendix A Mathematical Review.

Appendix B Summary of Convexity, Optimality Conditions, and Duality.

Bibliography.

Index.

作者简介

Mokhtar S. BAZARAA, PhD, is a Professor at the Georgia Institute of Technology.

HANIF D. SHERALI, PhD, is a W. Thomas Rice Chaired Professor of Engineering in the Grado Department of Industrial and Systems Engineering at Virginia Polytechnic Institute and State University.

C. M. SHETTY, PhD, is a Professor Emeritus at the Georgia Institute of Technology.

Professors Bazaraa and Sherali are also coauthors of the complementary bestselling book, Linear Programming and Network Flows, Third Edition, also published by Wiley.