Variational Analysis and Generalized Differentiation I

Basic Theory

  • Boris S. Mordukhovich

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 330)

Table of contents

  1. Front Matter
    Pages I-XXII
  2. Basic Theory

    1. Front Matter
      Pages 1-1
    2. Boris S. Mordukhovich
      Pages 3-170
    3. Boris S. Mordukhovich
      Pages 171-259
    4. Boris S. Mordukhovich
      Pages 261-375
  3. Back Matter
    Pages 477-579

About this book


Variational analysis is 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 nature. One of the most characteristic features of modern variational analysis is the intrinsic presence of nonsmoothness, which enters naturally not only through initial data of optimization-related problems but largely via variational principles and perturbation techniques. Thus generalized differential lies at the heart of variational analysis and its applications.

This monograph in two 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 the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc. The first of volume 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.


Banach and Asplund spaces Lipschitzian stability Variational analysis full calculus generalizes differentiation optimization sensitivity analysis

Authors and affiliations

  • Boris S. Mordukhovich
    • 1
  1. 1.College of Science, Department of MathematicsWayne State UniversityDetroitUSA

Bibliographic information