Variational Analysis and Applications

Description

Building on fundamental results in variational analysis, this monograph presents new and recent developments in the field as well as selected applications. Accessible to a broad spectrum of potential readers, the main material is presented in finite-dimensional spaces. Infinite-dimensional developments are discussed at the end of each chapter with comprehensive commentaries which emphasize the essence of major results, track the genesis of ideas, provide historical comments, and illuminate challenging open questions and directions for future research. The first half of the book (Chapters 1–6) gives a systematic exposition of key concepts and facts, containing basic material as well as some recent and new developments. These first chapters are particularly accessible to masters/doctoral students taking courses in modern optimization, variational analysis, applied analysis, variational inequalities, and variational methods. The reader’s development of skills will be facilitated as they work through each, or a portion of, the multitude of exercises of varying levels. Additionally, the reader may find hints and references to more difficult exercises and are encouraged to receive further inspiration from the gems in chapter commentaries. Chapters 7–10 focus on recent results and applications of variational analysis to advanced problems in modern optimization theory, including its hierarchical and multiobjective aspects, as well as microeconomics, and related areas. It will be of great use to researchers and professionals in applied and behavioral sciences and engineering. Front Matter ....Pages i-xix Constructions of Generalized Differentiation (Boris S. Mordukhovich)....Pages 1-66 Fundamental Principles of Variational Analysis (Boris S. Mordukhovich)....Pages 67-102 Well-Posedness and Coderivative Calculus (Boris S. Mordukhovich)....Pages 103-160 First-Order Subdifferential Calculus (Boris S. Mordukhovich)....Pages 161-190 Coderivatives of Maximal Monotone Operators (Boris S. Mordukhovich)....Pages 191-218 Nondifferentiable and Bilevel Optimization (Boris S. Mordukhovich)....Pages 219-258 Semi-infinite Programs with Some Convexity (Boris S. Mordukhovich)....Pages 259-349 Nonconvex Semi-infinite Optimization (Boris S. Mordukhovich)....Pages 351-449 Variational Analysis in Set Optimization (Boris S. Mordukhovich)....Pages 451-497 Set-Valued Optimization and Economics (Boris S. Mordukhovich)....Pages 499-532 Back Matter ....Pages 533-622