Variational analysis has been recognized as a fruitful area in mathematics that on the 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 natur. One of the most characteristic features of modern variational analysis is the intrinsic presence of nonsmoothness, which naturally enters not only through initial data of optimization-related problems but largely via variational principles and perturbation techniques. Thus generalized differential lies at the hear of variational analysis and its applications.

This monographs contains a comprehensive and 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 the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc. The book is published in two volumes, the first of which is mainly devoted to the basic theory of variational analysis and generalized differentiations, while the second volume contains various applications. Both volumes contain abundant bibliographies and extensive commentaries.

This book will be of interest to researchers and graduate students in mathematical sciences. It may also be useful to a broad range of researchers, practitioners, and graduate students involved in the study and applications of variational methods in economics, engineering, control systems, operations research, statistics, mechanics, and other applied sciences.

Autorentext

Ph.D. in Mathematics (1973); distinguished faculty and lifetime scholar of the Academy of Scholars; more than 200 publications (including books and patents); many outstanding research and teaching awards; numerous invited talks to various meetings (e.g., 15 keynote presentations during the last year); organizer of conference, special sessions, and issues of journals; Editorial Boards of 11 international journals; grants and awards from NSF, NATO, NSERC, BSF, Australian Research Council, etc.

Zusammenfassung

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

Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.

Inhalt
Constrained Optimization and Equilibria: Necessary Optimality Conditions in Nondifferentiable Programming. Mathematical Programs with Equilibrium Constraints. Multiobjective Optimization. Subextremality and Suboptimality at Linear Rate.- Optimal Control of Evolution Systems in Banach Spaces: Optimal Control of Discrete-Time and Continuous-time Evolution Inclusions. Necessary Optimality Conditions for Differential Inclusions without Relaxation. Maximum Principle for Continuous-Time Systems with Smooth Dynamics. Approximate Maximum Principle in Optimal Control.- Optimal Control of Distributed Systems: Optimization of Differential-Algebraic Inclusions with Delays. Neumann Boundary Control of Semilinear Constrained Hyperbolic Equations. Drichelet Boundary Control of Linear Constrained Hyperbolic Equations. Minimax Control of Parabolic Systems with Pointwise State Constraints.- Applications to Economics: Models of Welfare Economics. Second Welfare Theorem for Nonconvex Economics. Nonconvex Economics with Ordered Commodity Spaces. Further Extensions and Public Goods.- References.- Glossary of Notation.- Index of Statements.