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Nonlinear Programming

Part of Classics in Applied Mathematics

Author: Olvi L. Mangasarian, University of Wisconsin, Madison

Date Published: January 1995
availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
format: Paperback
isbn: 9780898713411

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Description

This reprint of the 1969 book of the same name is a concise, rigorous, yet accessible, account of the fundamentals of constrained optimization theory. Many problems arising in diverse fields such as machine learning, medicine, chemical engineering, structural design, and airline scheduling can be reduced to a constrained optimization problem. This book provides readers with the fundamentals needed to study and solve such problems. Beginning with a chapter on linear inequalities and theorems of the alternative, basics of convex sets and separation theorems are then derived based on these theorems. This is followed by a chapter on convex functions that includes theorems of the alternative for such functions. These results are used in obtaining the saddlepoint optimality conditions of nonlinear programming without differentiability assumptions.

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Product details
- Date Published: January 1995
- format: Paperback
- isbn: 9780898713411
- length: 236 pages
- dimensions: 229 x 150 x 11 mm
- weight: 0.301kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
Preface to the Classic Edition
1. The Nonlinear Programming Problem, Preliminary Concepts, and Notation
2. Linear Inequalities and Theorems of the Alternative
3. Convex Sets in Rn
4. Convex and Concave Functions
5. Saddlepoint Optimality Criteria in Nonlinear Programming Without Differentiability
6. Differentiable Convex and Concave Functions
7. Optimality Criteria in Nonlinear Programming with Differentiability
8. Duality in Nonlinear Programming
9. Generalizations of Convex Functions. Quasiconvex, Strictly Quasiconvex, and Pseudoconvex Functions
10. Optimality and Duality for Generalized Convex and Concave Functions
11. Optimality and Duality in the Presence of Nonlinear Equality Constraints
Appendix A. Vectors and Matrices
Appendix B. Resume of Some Topological Properties of Rn
Appendix C. Continuous and Semicontinuous Functions, Minima and Infima
Appendix D. Differentiable Functions, Mean-value and Implicit Function Theorems
Bibliography
Name Index
Subject Index.
Author
Olvi L. Mangasarian, University of Wisconsin, Madison