Nonlinear Programming Theory and Algorithms

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Edition: 3rd
Format: Hardcover
Pub. Date: 2006-05-05
Publisher(s): Wiley-Interscience
List Price: $210.83

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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. 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.

Author Biography

Mokhtar S. BAZARAA, PhD, is a Professor at the Georgia Institute of Technology. </p> <p>HANIF D. SHERALI, PhD, is a W. Thomas Rice Chaired Professor of Engineering in the Grado Department of Industrial and Systems Engineering at Virginia Polytechnic Institute and State University. <p>C. M. SHETTY, PhD, is a Professor Emeritus at the Georgia Institute of Technology. <p>Professors Bazaraa and Sherali are also coauthors of the complementary bestselling book, Linear Programming and Network Flows, Third Edition, also published by Wiley.

Table of Contents

Chapter 1. Introduction.
PART I: CONVEX ANALYSIS.
Chapter 2. Convex Sets.
Chapter 3. Convex Functions and Generalizations.
PART II: OPTIMALITY CONDITIONS AND DUALITY.
Chapter 4. The Fritz John and the Karush-Kuhn-Tucker Optimality Conditions.
Chapter 5. Constraint Qualifications.
Chapter 6. Lagrangian Duality and Saddle Point Optimality Conditions.
PART III: ALGORITHMS AND THEIR CONVERGENCE.
Chapter 7. The Concept of an Algorithm.
Chapter 8. Unconstrained Optimization.
Chapter 9. Penalty and Barrier Functions.
Chapter 10. Methods of Feasible Directions.
Chapter 11. Linear Complementary Problem, and Quadratic, Separable, Fractional, and Geometric Programming.
Appendix A: Mathematical Review.
Appendix B: Summary of Convexity, Optimality Conditions, and Duality.
Bi bliography.
Index.

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