Topological Aspects of Nonsmooth Optimization

  • Vladimir Shikhman

Part of the Springer Optimization and Its Applications book series (volume 64)

Also part of the Nonconvex Optimization and Its Applications book sub series (SOIANOIA, volume 64)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Vladimir Shikhman
    Pages 1-13
  3. Vladimir Shikhman
    Pages 63-123
  4. Vladimir Shikhman
    Pages 141-165
  5. Vladimir Shikhman
    Pages 167-174
  6. Back Matter
    Pages 185-193

About this book


This book deals with nonsmooth structures arising within the optimization setting. It considers four optimization problems, namely, mathematical programs with complementarity constraints, general semi-infinite programming problems, mathematical programs with vanishing constraints and bilevel optimization. The author uses the topological approach and topological invariants of corresponding feasible sets are investigated. Moreover, the critical point theory in the sense of Morse is presented and parametric and stability issues are considered. The material progresses systematically and establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nonsmoothness.


Topological Aspects of Nonsmooth Optimization will benefit researchers and graduate students in applied mathematics, especially those working in optimization theory, nonsmooth analysis, algebraic topology and singularity theory. ​


Nonsmooth Analysis Optimization theory topological invariants

Authors and affiliations

  • Vladimir Shikhman
    • 1
  1. 1., Mathematics, Section C,RWTH Aachen UniversityAachenGermany

Bibliographic information