Variational Analysis and Applications

  • Boris S. Mordukhovich

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Boris S. Mordukhovich
    Pages 1-66
  3. Boris S. Mordukhovich
    Pages 67-102
  4. Boris S. Mordukhovich
    Pages 103-160
  5. Boris S. Mordukhovich
    Pages 161-190
  6. Boris S. Mordukhovich
    Pages 191-218
  7. Boris S. Mordukhovich
    Pages 219-258
  8. Boris S. Mordukhovich
    Pages 259-349
  9. Boris S. Mordukhovich
    Pages 351-449
  10. Boris S. Mordukhovich
    Pages 451-497
  11. Boris S. Mordukhovich
    Pages 499-532
  12. Back Matter
    Pages 533-622

About this book


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.


first-order variational analysis monograph with exercises second-order variational analysis variational analysis applications control systems for partial differential equations

Authors and affiliations

  • Boris S. Mordukhovich
    • 1
  1. 1.Department of MathematicsWayne State UniversityDetroitUSA

Bibliographic information