Nonlinear Programming - Brossura

Mangasarian, Olvi L.

Brossura

ISBN 10: 0898713412 ISBN 13: 9780898713411

Casa editrice: Society for Industrial and Applied Mathematics, 1987

Riassunto

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.

Su questo libro

Descrizione del libro

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 scheduling can be reduced to a constrained optimization problem. Provides readers with the fundamentals needed to study and solve such problems.

Contenuti

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.

Dettagli dell?edizione

• Editore: Society for Industrial and Applied Mathematics
• Data di pubblicazione: 1987
• ISBN 10: 0898713412
• ISBN 13: 9780898713411
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 236