Nonlinear Programming: Theory and Algorithms / Edition 2

Nonlinear Programming: Theory and Algorithms / Edition 2

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

ISBN-10: 0471557935

ISBN-13: 9780471557937

Pub. Date: 11/01/1992

Publisher: Wiley

Presents recent developments of key topics in nonlinear programming using a logical and self-contained format. Divided into three sections that deal with convex analysis, optimality conditions and duality, computational techniques. Precise statements of algorithms are given along with convergence analysis. Each chapter contains detailed numerical examples, graphical…  See more details below

Overview

Presents recent developments of key topics in nonlinear programming using a logical and self-contained format. Divided into three sections that deal with convex analysis, optimality conditions and duality, computational techniques. Precise statements of algorithms are given along with convergence analysis. Each chapter contains detailed numerical examples, graphical illustrations and numerous exercises to aid readers in understanding the concepts and methods discussed.

Product Details

ISBN-13:
9780471557937
Publisher:
Wiley
Publication date:
11/01/1992
Series:
Interscience Series in Discrete Mathematics
Edition description:
Older Edition
Pages:
656
Product dimensions:
7.32(w) x 10.23(h) x 1.37(d)

Table of Contents

Ch. 1Introduction1
1.1Problem Statement and Basic Definitions2
1.2Some Illustrative Examples4
1.3Some Guidelines for Model Construction21
Pt. 1Convex Analysis31
Ch. 2Convex Sets33
2.1Convex Hulls34
2.2Closure and Interior of a Set38
2.3Weierstrass' Theorem41
2.4Separation and Support of Sets42
2.5Convex Cones and Polarity52
2.6Polyhedral Sets, Extreme Points, and Extreme Directions54
2.7Linear Programming and the Simplex Method62
Ch. 3Convex Functions and Generalizations78
3.1Definitions and Basic Properties79
3.2Subgradients of Convex Functions83
3.3Differentiable Convex Functions88
3.4Minima and Maxima of Convex Functions99
3.5Generalizations of Convex Functions107
Pt. 2Optimality Conditions and Duality129
Ch. 4The Fritz John and the Karush-Kuhn-Tucker Optimality Conditions131
4.1Unconstrained Problems132
4.2Problems with Inequality Constraints138
4.3Problems with Inequality and Equality Constraints156
4.4Second-Order Necessary and Sufficient Optimality Conditions for Constrained Problems167
Ch. 5Constraint Qualifications184
5.1The Cone of Tangents184
5.2Other Constraint Qualifications188
5.3Problems with Inequality and Equality Constraints191
Ch. 6Lagrangian Duality and Saddle Point Optimality Conditions199
6.1The Lagrangian Dual Problem200
6.2Duality Theorems and Saddle Point Optimality Conditions203
6.3Properties of the Dual Function214
6.4Formulating and Solving the Dual Problem222
6.5Getting the Primal Solution228
6.6Linear and Quadratic Programs231
Pt. 3Algorithms and Their Convergence243
Ch. 7The Concept of an Algorithm244
7.1Algorithms and Algorithmic Maps244
7.2Closed Maps and Convergence247
7.3Composition of Mappings251
7.4Comparison Among Algorithms255
Ch. 8Unconstrained Optimization265
8.1Line Search Without Using Derivatives266
8.2Line Search Using Derivatives276
8.3Some Practical Line Search Methods279
8.4Closedness of the Line Search Algorithmic Map282
8.5Multidimensional Search Without Using Derivatives283
8.6Multidimensional Search Using Derivatives300
8.7Modification of Newton's Method: Levenberg-Marquardt and Trust Region Methods312
8.8Methods Using Conjugate Directions: Quasi-Newton and Conjugate Gradient Methods315
8.9Subgradient Optimization Methods339
Ch. 9Penalty and Barrier Functions360
9.1The Concept of Penalty Functions361
9.2Exterior Penalty Function Methods365
9.3Exact Absolute Value and Augmented Lagrangian Penalty Methods372
9.4Barrier Function Methods385
9.5A Polynomial-Time Algorithm for Linear Programming Based on a Barrier Function392
Ch. 10Methods of Feasible Directions408
10.1The Method of Zoutendijk409
10.2Convergence Analysis of the Method of Zoutendijk423
10.3Successive Linear Programming Approach432
10.4Successive Quadratic Programming or Projected Lagrangian Approach438
10.5The Gradient Projection Method of Rosen448
10.6The Method of Reduced Gradient of Wolfe and the Generalized Reduced Gradient Method458
10.7The Convex-Simplex Method of Zangwill466
10.8Effective First- and Second-Order Variants of the Reduced Gradient Method471
Ch. 11Linear Complementary Problem, and Quadratic, Separable, Fractional, and Geometric Programming493
11.1The Linear Complementary Problem494
11.2Quadratic Programming503
11.3Separable Programming509
11.4Linear Fractional Programming524
11.5Geometric Programming531
Appendix A. Mathematical Review554
Appendix B. Summary of Convexity, Optimality Conditions, and Duality565
Bibliography576
Index627

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