Variational Analysis of Regular Mappings

Theory and Applications

  • Alexander D. Ioffe

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

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Alexander D. Ioffe
    Pages 1-31
  3. Alexander D. Ioffe
    Pages 33-97
  4. Alexander D. Ioffe
    Pages 99-140
  5. Alexander D. Ioffe
    Pages 141-193
  6. Alexander D. Ioffe
    Pages 195-243
  7. Alexander D. Ioffe
    Pages 245-298
  8. Alexander D. Ioffe
    Pages 299-364
  9. Alexander D. Ioffe
    Pages 365-414
  10. Alexander D. Ioffe
    Pages 415-476
  11. Back Matter
    Pages 477-495

About this book


This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory.

The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, which have proven to be highly efficient even in classical settings, and outlines the theory’s predominantly quantitative character, leading to a variety of new and unexpected applications.

Variational Analysis of Regular Mappings is aimed at graduate students and researchers in nonlinear and functional analysis, especially those working in areas close to optimization and optimal control, and will be suitable to anyone interested in applying new concepts and ideas to operations research, control engineering and numerical analysis.


metric regularity error bound perturbation stability analysis perturbation theory stability set-valued mappings generalized equations variational inequalities over polyhedral sets mappings with special structures necessary optimality conditions necessary optimality conditions in constraint metric fixed point theory distance metric theory regularity theory math alternating projections for convex sets alternating projections for nonconvex sets non-differentiable functions curves of descent calculus of subdifferentials calculus of coderivatives

Authors and affiliations

  • Alexander D. Ioffe
    • 1
  1. 1.Department of MathematicsTechnion – Israel Institute of TechnologyHaifaIsrael

Bibliographic information