Nonlinear programming : theory and algorithms

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

資料種別:

図書

出版情報:

New York : Wiley, c1979

形態:

xiv, 560 p. ; 24 cm

著者名:

ISBN:

9780471786108 [0471786101]

書誌ID:

BA03008818

子書誌情報

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他の版・巻

Nonlinear programming : theory and algorithms. 2nd ed (: hard ; : pbk)
Mokhtar S. Bazaraa, Hanif D. Sherali, C.M. Shetty , Wiley , c1993

書誌詳細

注記:

Bibliography: p. [516]-552
Includes index

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. / 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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