Nonlinear Programming: (Classics in Applied Mathematics)

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. Properties of differentiable convex functions are derived and then used in two key chapters of the book, one on optimality conditions for differentiable nonlinear programs and one on duality in nonlinear programming. Generalizations of convex functions to pseudoconvex and quasiconvex functions are given and then used to obtain generalized optimality conditions and duality results in the presence of nonlinear equality constraints. The book has four useful self-contained appendices on vectors and matrices, topological properties of n-dimensional real space, continuity and minimization, and differentiable functions.

Table of Contents:
Preface to the Classics Edition Preface Chapter 1: The Nonlinear Programming Problem, Preliminary Concepts, and Notation Chapter 2: Linear Inequalities and Theorems of the Alternative Chapter 3: Convex Sets in Rn Chapter 4: Convex and Concave Functions Chapter 5: Saddlepoint Optimality Criteria of Nonlinear Programming Without Differentiability Chapter 6: Differentiable Convex and Concave Functions Chapter 7: Optimality Criteria in Nonlinear Programming with Differentiability Chapter 8: Duality in Nonlinear Programming Chapter 9: Generalizations of Convex Functions: Quasiconvex, Strictly Quasiconvex, and Pseudoconvex Functions Chapter 10: Optimality and Duality for Generalized Convex and Concave Functions Chapter 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.