附註:Includes bibliographical references (pages 311-324) and index.
Cover -- Table of Contents -- Introduction -- List of Results -- Basic Notation -- 1 Basic Concepts -- 1.1 Formal Settings -- 1.2 Multifunctions and Derivatives -- 1.3 Particular Locally Lipschitz Functions and Related Definitions -- 1.4 Definitions of Regularity -- 1.5 Related Definitions -- 1.6 First Motivations -- 2 Regularity and Consequences -- 2.1 Upper Regularity at Points and Sets -- 2.2 Pseudo-Regularity -- 3 Characterizations of Regularity by Derivatives -- 3.1 Strong Regularity and Thibault's Limit Sets -- 3.2 Upper Regularity and Contingent Derivatives -- 3.3 Pseudo-Regularity and Generalized Derivatives -- 4 Nonlinear Variations and Implicit Functions -- 4.1 Successive Approximation and Persistence of Pseudo-Regularity -- 4.2 Persistence of Upper Regularity -- 4.3 Implicit Functions -- 5 Closed Mappings in Finite Dimension -- 5.1 Closed Multifunctions in Finite Dimension -- 5.2 Continuous and Locally Lipschitz Functions -- 5.3 Implicit Lipschitz Functions on Rn -- 6 Analysis of Generalized Derivatives -- 6.1 General Properties for Abstract and Polyhedral Mappings -- 6.2 Derivatives for Lipschitz Functions in Finite Dimension -- 6.3 Relations between Tf and 8f -- 6.4 Chain Rules of Equation Type -- 6.5 Mean Value Theorems, Taylor Expansion and Quadratic Growth -- 6.6 Contingent Derivatives of Implicit (Multi ...) Functions and Stationary Points -- 7 Critical Points and Generalized Kojima ... Functions -- 7.1 Motivation and Definition -- 7.2 Examples and Canonical Parametrizations -- 7.3 Derivatives and Regularity of Generalized Kojima ... Functions -- 7.4 Discussion of Particular Cases -- 7.5 Pseudo ... Regularity versus Strong Regularity -- 8 Parametric Optimization Problems -- 8.1 The Basic Model -- 8.2 Critical Points under Perturbations -- 8.3 Stationary and Optimal Solutions under Perturbations -- 8.4 Taylor Expansion of Critical Values -- 9 Derivatives and Regularity of Further Nonsmooth Maps -- 9.1 Generalized Derivatives for Positively Homogen
摘要:The book establishes links between regularity and derivative concepts of nonsmooth analysis and studies of solution methods and stability for optimization, complementarity and equilibrium problems. In developing necessary tools, it presents, in particular: an extended analysis of Lipschitz functions and the calculus of their generalized derivatives, including regularity, successive approximation and implicit functions for multivalued mappings; a unified theory of Lipschitzian critical points in optimization and other variational problems, with relations to reformulations by penalty, barrier and NCP functions; an analysis of generalized Newton methods based on linear and nonlinear approximations; the interpretation of hypotheses, generalized derivatives and solution methods in terms of original data and quadratic approximations; a rich collection of instructive examples and exercises./LIST Audience: Researchers, graduate students and practitioners in various fields of applied mathematics, engineering, OR and economics. Also university teachers and advanced students who wish to get insights into problems, future directions and recent developments.
