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

Format:

Book

Author/Creator:

Bazaraa, M. S.

Contributor:

Sherali, Hanif D., 1952-

Shetty, C. M., 1929-

Engineering Book Fund.

Language:

English

Subjects (All):

Nonlinear programming.

Physical Description:

xv, 853 pages : illustrations ; 25 cm

Edition:

Third edition.

Place of Publication:

Hoboken, N.J. : Wiley-Interscience, [2006]

Summary:

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.

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.

Contents:

1.1 Problem Statement and Basic Definitions 2

1.3 Guidelines for Model Construction 26

Part 1 Convex Analysis 37

Chapter 2 Convex Sets 39

2.1 Convex Hulls 40

2.2 Closure and Interior of a Set 45

2.3 Weierstrass's Theorem 48

2.4 Separation and Support of Sets 50

2.5 Convex Cones and Polarity 62

2.6 Polyhedral Sets, Extreme Points, and Extreme Directions 64

2.7 Linear Programming and the Simplex Method 75

Chapter 3 Convex Functions and Generalizations 97

3.1 Definitions and Basic Properties 98

3.2 Subgradients of Convex Functions 103

3.3 Differentiable Convex Functions 109

3.4 Minima and Maxima of Convex Functions 123

3.5 Generalizations of Convex Functions 134

Part 2 Optimality Conditions and Duality 163

Chapter 4 The Fritz John and Karush-Kuhn-Tucker Optimality Conditions 165

4.1 Unconstrained Problems 166

4.2 Problems Having Inequality Constraints 174

4.3 Problems Having Inequality and Equality Constraints 197

4.4 Second-Order Necessary and Sufficient Optimality Conditions for Constrained Problems 211

Chapter 5 Constraint Qualification 237

5.1 Cone of Tangents 237

5.2 Other Constraint Qualifications 241

5.3 Problems Having Inequality and Equality Constraints 245

Chapter 6 Lagrangian Duality and Saddle Point Optimality Conditions 257

6.1 Lagrangian Dual Problem 258

6.2 Duality Theorems and Saddle Point Optimality Conditions 263

6.3 Properties of the Dual Function 276

6.4 Formulating and Solving the Dual Problem 286

6.5 Getting the Primal Solution 293

6.6 Linear and Quadratic Programs 298

Part 3 Algorithms and Their Convergence 315

Chapter 7 The Concept of an Algorithm 317

7.1 Algorithms and Algorithmic Maps 317

7.2 Closed Maps and Convergence 319

7.3 Composition of Mappings 324

7.4 Comparison Among Algorithms 329

Chapter 8 Unconstrained Optimization 343

8.1 Line Search Without Using Derivatives 344

8.2 Line Search Using Derivatives 356

8.3 Some Practical Line Search Methods 360

8.4 Closedness of the Line Search Algorithmic Map 363

8.5 Multidimensional Search Without Using Derivatives 365

8.6 Multidimensional Search Using Derivatives 384

8.7 Modification of Newton's Method: Levenberg-Marquardt and Trust Region Methods 398

8.8 Methods Using Conjugate Directions: Quasi-Newton and Conjugate Gradient Methods 402

8.9 Subgradient Optimization Methods 435

Chapter 9 Penalty and Barrier Functions 469

9.1 Concept of Penalty Functions 470

9.2 Exterior Penalty Function Methods 475

9.3 Exact Absolute Value and Augmented Lagrangian Penalty Methods 485

9.4 Barrier Function Methods 501

9.5 Polynomial-Time Interior Point Algorithms for Linear Programming Based on a Barrier Function 509

Chapter 10 Methods of Feasible Directions 537

10.1 Method of Zoutendijk 538

10.2 Convergence Analysis of the Method of Zoutendijk 557

10.3 Successive Linear Programming Approach 568

10.4 Successive Quadratic Programming or Projected Lagrangian Approach 576

10.5 Gradient Projection Method of Rosen 589

10.6 Reduced Gradient Method of Wolfe and Generalized Reduced Gradient Method 602

10.7 Convex-Simplex Method of Zangwill 613

10.8 Effective First- and Second-Order Variants of the Reduced Gradient Method 620

Chapter 11 Linear Complementary Problem, and Quadratic, Separable, Fractional, and Geometric Programming 655

11.1 Linear Complementary Problem 656

11.2 Convex and Nonconvex Quadratic Programming: Global Optimization Approaches 667

11.3 Separable Programming 684

11.4 Linear Fractional Programming 703

11.5 Geometric Programming 712

Appendix A Mathematical Review 751

Appendix B Summary of Convexity, Optimality Conditions, and Duality 765.

Notes:

Includes bibliographical references (pages 779-841) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Engineering Book Fund.

ISBN:

0471486000

OCLC:

61478842

Publisher Number:

9780471486008

Online:

Publisher description