Variational Analysis and Applications

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.

Preface.- Part 1. Basics of First-Order Analysis.-1. First-Order Generalized Differentiation.- 2. Extremality, Well-Posedness, Calculus Rules.- 3. Optimization via Generalized Differentiation.- Part 2. Second-Order Analysis.- 4. Second-Order Subdifferentials.- 5. Second-Order Subdifferential Calculus.- 6. Full and Tilt Stability of Local Minimizers.- 7. Full Stability for Parametric Variational Systems.- Part 3. Selected Applications.- 8. Full and Tilt Stability in Constrained Optimization.-9. Higher-Order Stability and Numerical Analysis.- 10. Optimal Control of the Sweeping Process.- 11. Microeconomic Modeling.- References.- List of Statements.- Glossary of Notation.- Subject Index.