Principles of optimization theory / C.R. Bector, S. Chandra, J. Dutta.

Includes bibliographical references (pages 217-221) and index.

Introduction Optimization: A Little History Definitions and Basic Facts Conditions for a Minimum/ Elements of Convex Analysis Convex Sets and Separation Theorems Polyhedral Convex Sets and Farkas lemma/ Convex Functions: basic Properties and Generalization Subdifferentials and Calculus Rules Tangent and Normal Cones Theorems of the Alternative Karush-Kuhn-Tucker Conditions Unconstrained Minimization Fritz-John Conditios Karush-Kuhn-Tucker Conditions Generalized Convexity and Sufficiency Equality Constraints Convex Optimization The Basic Problem Convex Optimization with Inequality Constraints Saddle Point Conditions Convex Optimization with Mixed Constraints Nonsmooth Optimization Clarke Subdifferential and Related Results Clarke Tangent and Normal Cones Optimality Conditions in Lipschitz Optimization Applications to Strict Minimization Generalized Convexity and Nonsmoothness Quasidifferentials and Optimality Conditions Subdifferentials of Non-Lipschitz Functions: Some Ideas Duality The Value Function and Lagrangian Duality Fenchel Duality Fractional Programming Duality Nonlinear Lagrangian and Nonconvex Duality Monotone and Generalized Monotone Maps Motivation Convexity and Monotonicity Subdifferential as a Monotone Map Quasimonotone and Pseudomonotone maps Bibliography Index