Nonlinear programming : theory and algorithms

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Nonlinear programming : theory and algorithms / Mokhtar S. Bazaraa, Hanif D. Sherali, C.M. Shetty

版:

3rd ed

資料種別:

電子ブック

出版情報:

Wiley Online Library, 2005

形態:

1 online resource (xv, 853p)

シリーズ名:

A Wiley-Interscience publication <BA00493885>

著者名:

ISBN:

9780471787778 [0471787779] (: electronic bk)

書誌ID:

TT00015624

子書誌情報

フルテキスト

所蔵情報

書誌詳細

注記:

Includes bibliographical references (p. 779-841) and index
Print published: Hoboken, N.J. : Wiley , c2006

主題:

Nonlinear programming

言語:

英語

目次情報:

Introduction. / Chapter 1：

Problem Statement and Basic Definitions / 1.1：

Illustrative Examples / 1.2：

Guidelines for Model Construction / 1.3：

Exercises

Notes and References

Convex Analysis. / Part 1：

Convex Sets. / Chapter 2：

Convex Hulls / 2.1：

Closure and Interior of a Set / 2.2：

Weierstrass's Theorem / 2.3：

Separation and Support of Sets / 2.4：

Convex Cones and Polarity / 2.5：

Polyhedral Sets, Extreme Points, and Extreme Directions / 2.6：

Linear Programming and the Simplex Method / 2.7：

Convex Functions and Generalizations. / Chapter 3：

Definitions and Basic Properties / 3.1：

Subgradients of Convex Functions / 3.2：

Differentiable Convex Functions / 3.3：

Minima and Maxima of Convex Functions / 3.4：

Generalizations of Convex Functions / 3.5：

Optimality Conditions and Duality. / Part 2：

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

Unconstrained Problems / 4.1：

Problems Having Inequality Constraints / 4.2：

Problems Having Inequality and Equality Constraints / 4.3：

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

Constraint Qualifications. / Chapter 5：

Cone of Tangents / 5.1：

Other Constraint Qualifications / 5.2：

Lagrangian Duality and Saddle Point Optimality Conditions. / 5.3：

Lagrangian Dual Problem / 6.1：

Duality Theorems and Saddle Point Optimality Conditions / 6.2：

Properties of the Dual Function / 6.3：

Formulating and Solving the Dual Problem / 6.4：

Getting the Primal Solution / 6.5：

Linear and Quadratic Programs / 6.6：

Algorithms and Their Convergence / Part 3：

The Concept of an Algorithm. / Chapter 7：

Algorithms and Algorithmic Maps / 7.1：

Closed Maps and Convergence / 7.2：

Composition of Mappings / 7.3：

Comparison Among Algorithms / 7.4：

Unconstrained Optimization. / Chapter 8：

Line Search Without Using Derivatives / 8.1：

Line Search Using Derivatives / 8.2：

Some Practical Line Search Methods / 8.3：

Closedness of the Line Search Algorithmic Map / 8.4：

Multidimensional Search Without Using Derivatives / 8.5：

Multidimensional Search Using Derivatives / 8.6：

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

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

Subgradient Optimization Methods / 8.9：

Penalty and Barrier Functions. / Chapter 9：

Concept of Penalty Functions / 9.1：

Exterior Penalty Function Methods / 9.2：

Exact Absolute Value and Augmented Lagrangian Penalty Methods / 9.3：

Barrier Function Methods / 9.4：

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

Methods of Feasible Directions. / Chapter 10：

Method of Zoutendijk / 10.1：

Convergence Analysis of the Method of Zoutendijk / 10.2：

Successive Linear Programming Approach / 10.3：

Successive Quadratic Programming or Projected Lagrangian Approach / 10.4：

Gradient Projection Method of Rosen / 10.5：

Reduced Gradient Method of Wolfe and Generalized Reduced Gradient Method / 10.6：

Convex-Simplex Method of Zangwill / 10.7：

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

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

Linear Complementary Problem / 11.1：

Convex and Nonconvex Quadratic Programming: Global Optimization Approaches / 11.2：

Separable Programming / 11.3：

Linear Fractional Programming / 11.4：

Geometric Programming / 11.5：

Mathematical Review. / Appendix A：

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

Bibliography.

Index

Introduction

Convex Analysis

Convex Sets

Convex Functions and Generalizations

Optimality Conditions and Duality

The Fritz John and Karush-Kuhn-Tucker Optimality Conditions

Constraint Qualification

Lagrangian Duality and Saddle Point Optimality Conditions

The Concept of an Algorithm

Unconstrained Optimization

Penalty and Barrier Functions

Methods of Feasible Directions

Linear Complementary Problem, and Quadratic, Separable, Fractional, and Geometric Programming

Mathematical Review

Summary of Convexity, Optimality Conditions, and Duality

Bibliography

Introduction. / Chapter 1：

Problem Statement and Basic Definitions / 1.1：

Illustrative Examples / 1.2：

Guidelines for Model Construction / 1.3：

Exercises

Notes and References

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