Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization

ISBN: 9781439868201 出版年：2013 页码：294 Ansari, Qamrul Hasan Lalitha, C S Mehta, Monika CRC Press

Generalized Convexity and Generalized Monotonicity Elements of Convex Analysis Preliminaries and Basic Concepts Convex Sets Hyperplanes Convex Functions Generalized Convex Functions Optimality Criteria Subgradients and Subdifferentials Generalized Derivatives and Generalized Subdifferentials Directional Derivatives Gateaux Derivatives Dini and Dini-Hadamard Derivatives Clarke and Other Types of Derivatives Dini and Clarke Subdifferentials Nonsmooth Convexity Nonsmooth Convexity in Terms of Bifunctions Generalized Nonsmooth Convexity in Terms of Bifunctions Generalized Nonsmooth Convexity in Terms of Subdifferentials Generalized Nonsmooth Pseudolinearity in Terms of Clarke Subdifferentials Monotonocity and Generalized Monotonicity Monotonicity and Its Relation with Convexity Nonsmooth Monotonicity and Generalized Monotonicity in Terms of a Bifunction Relation between Nonsmooth Monotonicity and Nonsmooth Convexity Nonsmooth Pseudoaffine Bifunctions and Nonsmooth Pseudolinearity Generalized Monotonicity for Set-Valued Maps Nonsmooth Variational Inequalities and Nonsmooth Optimization Elements of Variational Inequalities Variational Inequalities and Related Problems Basic Existence and Uniqueness Results Gap Functions Solution Methods Nonsmooth Variational Inequalities Nonsmooth Variational Inequalities in Terms of a Bifunction Relation between an Optimization Problem and Nonsmooth Variational Inequalities Existence Criteria Extended Nonsmooth Variational Inequalities Gap Functions and Saddle Point Characterization Characterizations of Solution Sets of Optimization Problem and Nonsmooth Variational Inequalities Characterizations of the Solution Set of an Optimization Problem with a Pseudolinear Objective Function Characterizations of the Solution Set of Variational Inequalities Involving Pseudoaffine Bifunctions Lagrange Multiplier Characterizations of Solution Set of an Optimization Problem Nonsmooth Generalized Variational Inequalities and Optimization Problems Generalized Variational Inequalities and Related Topics Basic Existence and Uniqueness Results Gap Functions for Generalized Variational Inequalities Generalized Variational Inequalities in Terms of the Clarke Subdifferential and Optimization Problems Characterizations of Solution Sets of an Optimization Problem with Generalized Pseudolinear Objective Function Appendix A: Set-Valued Maps Appendix B: Elements of Nonlinear Analysis Index