VARIATIONAL ANALYSIS AND GENERALIZED DIFFERENTIATION 1

Variational analysis is a fruitful area in mathematics that, on one hand, deals with the study of optimization and equilibrium problems and, on the other hand, applies optimization, perturbation, and approximation ideas to the analysis of a broad range of problems that may not be of a variational nature. This monograph in 2 volumes contains a comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces and presents numerous applications to problems in optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc. The first volume is devoted to the basic theory of variational analysis and generalized differentiations, while the second volume describes various applications. Both volumes include abundant bibliographies and extensive commentaries. TOC:Generalized Differentiation in Banach Spaces: Generalized Normals to Nonconvex Sets. Coderivatives of Set-Valued Mappings. Subdifferentials of Nonsmooth Functions.- Extremal Principle in Variational Analysis: Set Extremality and Nonconvex Separation. Extremal Principle in Asplund Spaces. Relations with Variational Principles. Representations and Characterizations in Asplund Spaces. Versions of the Extremal Principle in Banach Spaces.- Full Calculus in Asplund Spaces: Calculus Rules for Normals and Coderivatives. Subdifferential Calculus and Related Topics. SNC Calculus for Sets and Mappings.- Lipschitzian Stability and Sensivity Analysis: Neighborhood Criteria and Exact Bounds. Pointbased Characterizations. Sensitivity Analysis for Constraint Systems. Sensitivity Analysis for Variational Systems.- References.- Glossary of Notation.- Index of Statements.