Nonlinear Programming: Theory and Algorithms, 3/e (Hardcover)

Mokhtar S. Bazaraa, Hanif D. Sherali, C. M. Shetty

  • 出版商: Wiley
  • 出版日期: 2006-04-01
  • 售價: $7,360
  • 貴賓價: 9.5$6,992
  • 語言: 英文
  • 頁數: 872
  • 裝訂: Hardcover
  • ISBN: 0471486000
  • ISBN-13: 9780471486008
  • 相關分類: R 語言Algorithms-data-structures
  • 海外代購書籍(需單獨結帳)
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商品描述

Description

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.

 

Table of Contents

Chapter 1 Introduction.

1.1 Problem Statement and Basic Definitions.

1.2 Illustrative Examples.

1.3 Guidelines for Model Construction.

Exercises.

Notes and References.

Part 1 Convex Analysis.

Chapter 2 Convex Sets.

2.1 Convex Hulls.

2.2 Closure and Interior of a Set.

2.3 Weierstrass's Theorem.

2.4 Separation and Support of Sets.

2.5 Convex Cones and Polarity.

2.6 Polyhedral Sets, Extreme Points, and Extreme Directions.

2.7 Linear Programming and the Simplex Method.

Exercises.

Notes and References.

Chapter 3 Convex Functions and Generalizations.

3.1 Definitions and Basic Properties.

3.2 Subgradients of Convex Functions.

3.3 Differentiable Convex Functions.

3.4 Minima and Maxima of Convex Functions.

3.5 Generalizations of Convex Functions.

Exercises.

Notes and References.

Part 2 Optimality Conditions and Duality.

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

4.1 Unconstrained Problems.

4.2 Problems Having Inequality Constraints.

4.3 Problems Having Inequality and Equality Constraints.

4.4 Second-Order Necessary and Sufficient Optimality Conditions for Constrained Problems.

Exercises.

Notes and References.

Chapter 5 Constraint Qualifications.

5.1 Cone of Tangents.

5.2 Other Constraint Qualifications.

5.3 Problems Having Inequality and Equality Constraints.

Exercises.

Notes and References.

Chapter 6 Lagrangian Duality and Saddle Point Optimality Conditions.

6.1 Lagrangian Dual Problem.

6.2 Duality Theorems and Saddle Point Optimality Conditions.

6.3 Properties of the Dual Function.

6.4 Formulating and Solving the Dual Problem

6.5 Getting the Primal Solution.

6.6 Linear and Quadratic Programs.

Exercises.

Notes and References.

Part 3 Algorithms and Their Convergence.

Chapter 7 The Concept of an Algorithm.

7.1 Algorithms and Algorithmic Maps.

7.2 Closed Maps and Convergence.

7.3 Composition of Mappings.

7.4 Comparison Among Algorithms.

Exercises.

Notes and References.

Chapter 8 Unconstrained Optimization.

8.1 Line Search Without Using Derivatives.

8.2 Line Search Using Derivatives.

8.3 Some Practical Line Search Methods.

8.4 Closedness of the Line Search Algorithmic Map.

8.5 Multidimensional Search Without Using Derivatives.

8.6 Multidimensional Search Using Derivatives.

8.7 Modification of Newton's Method: Levenberg-Marquardt and Trust Region Methods.

8.8 Methods Using Conjugate Directions: Quasi-Newton and Conjugate Gradient Methods.

8.9 Subgradient Optimization Methods.

Exercises.

Notes and References.

Chapter 9 Penalty and Barrier Functions.

9.1 Concept of Penalty Functions.

9.2 Exterior Penalty Function Methods.

9.3 Exact Absolute Value and Augmented Lagrangian Penalty Methods.

9.4 Barrier Function Methods.

9.5 Polynomial-Time Interior Point Algorithms for Linear Programming Based on a Barrier Function.

Exercises.

Notes and References.

Chapter 10 Methods of Feasible Directions.

10.1 Method of Zoutendijk.

10.2 Convergence Analysis of the Method of Zoutendijk.

10.3 Successive Linear Programming Approach.

10.4 Successive Quadratic Programming or Projected Lagrangian Approach.

10.5 Gradient Projection Method of Rosen.

10.6 Reduced Gradient Method of Wolfe and Generalized Reduced Gradient Method.

10.7 Convex-Simplex Method of Zangwill.

10.8 Effective First- and Second-Order Variants of the Reduced Gradient Method.

Exercises.

Notes and References.

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

1 1.1 Linear Complementary Problem.

1 1.2 Convex and Nonconvex Quadratic Programming: Global Optimization Approaches.

11.3 Separable Programming.

1 1.4 Linear Fractional Programming.

1 1.5 Geometric Programming.

Exercises.

Notes and References.

Appendix A Mathematical Review.

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

Bibliography.

Index.

商品描述(中文翻譯)

《非線性規劃:理論與演算法》是一本全面介紹非線性規劃理論和演算法的書籍,經過全面修訂和擴充的第三版。該書討論了在等式和不等式約束存在的情況下優化目標函數的問題。由於目標函數的非線性性質和/或約束的非線性性質,許多現實問題無法適當地表示為線性規劃。第三版首先通過具體示例和模型構建指南對非線性規劃進行了一般介紹。

該書重點介紹了非線性規劃的三個主要部分:
1. 凸分析,包括凸集的拓撲性質、凸集的分離和支撐、多面體集合、多面體集合的極點和極方向,以及線性規劃。
2. 最優性條件和對偶性,包括經典的Fritz John(FJ)和Karush-Kuhn-Tucker(KKT)最優性條件的性質、解釋和價值;各種提出的約束資格之間的相互關係;以及拉格朗日對偶性和鞍點最優性條件。
3. 演算法及其收斂性,介紹了解決無約束和有約束非線性規劃問題的演算法。

第三版的重要特點包括:
- 新的主題,如第二內點法、非凸優化、非可微優化等。
- 每章的更新討論和新應用。
- 詳細的數值示例和圖形說明。
- 對建模和構建非線性規劃問題的重要覆蓋。
- 簡單的數值問題。
- 高級理論練習題。

該書是專業人士的可靠參考資料,也是運籌學、管理科學、工業工程、應用數學以及涉及分析優化技術的工程學科的學生的有用教材。該書以邏輯和自包含的格式獨特地涵蓋了非線性規劃技術,提供了豐富的信息、寶貴的示例和插圖,展示了非線性問題中最新的進展。

該書的目錄如下:
1. 引言
1.1 問題陳述和基本定義
1.2 具體示例
1.3 模型構建指南
練習題
註解和參考資料

以上是對該書的翻譯,希望對台灣讀者有所幫助。