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  • © 2012

Topological Aspects of Nonsmooth Optimization

Authors:

  • Establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nonsmoothness
  • Considers four optimization problems and uses a topological approach ?
  • Handles various equilibrium optimization problems from the same topological point of view
  • Links ideas from singularity and transversality theory with nonsmooth optimization
  • Includes supplementary material: sn.pub/extras

Part of the book series: Nonconvex Optimization and Its Applications (SOIANOIA, volume 64)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xi
  2. Introduction

    • Vladimir Shikhman
    Pages 1-13
  3. General Semi-infinite Programming Problems

    • Vladimir Shikhman
    Pages 63-123
  4. Bilevel Optimization

    • Vladimir Shikhman
    Pages 141-165
  5. Impacts on Nonsmooth Analysis

    • 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. ​

Reviews

From the reviews:

“This monograph … provides detailed topological investigations of nonsmooth optimization problems. … the book highlights and motivates recent developments in a broad field of active research. The material is well presented, so that the book may be warmly recommended to graduate students and researchers in optimization.” (Oliver Stein, Mathematical Reviews, October, 2013)

“The textbook (PhD thesis of the author) deals with mathematical programming problems which have smooth data but show, because of their structure, intrinsic non-smooth behavior … . It can be used as a compendium of the critical-point theory also in the smooth case since nearly all important results are cited. New results are proved or it is referred to recently published results of the author. For researchers in the above described field of mathematical programming the book will become a very helpful and indispensable tool.” (Armin Hoffmann, Zentralblatt MATH, Vol. 1234, 2012)

Authors and Affiliations

  • , Mathematics, Section C,, RWTH Aachen University, Aachen, Germany

    Vladimir Shikhman

Bibliographic Information

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access