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Conjugate Duality in Convex Optimization

  • Radu Ioan Bot

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 637)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Radu Ioan Boţ
    Pages 1-8
  3. Radu Ioan Boţ
    Pages 9-33
  4. Radu Ioan Boţ
    Pages 65-86
  5. Radu Ioan Boţ
    Pages 87-103
  6. Radu Ioan Boţ
    Pages 105-131
  7. Back Matter
    Pages 157-164

About this book

Introduction

This book presents new achievements and results in the theory of conjugate duality for convex optimization problems. The perturbation approach for attaching a dual problem to a primal one makes the object of a preliminary chapter, where also an overview of the classical generalized interior point regularity conditions is given. A central role in the book is played by the formulation of generalized Moreau-Rockafellar formulae and closedness-type conditions, the latter constituting a new class of regularity conditions, in many situations with a wider applicability than the generalized interior point ones. The reader also receives deep insights into biconjugate calculus for convex functions, the relations between different existing strong duality notions, but also into several unconventional Fenchel duality topics. The final part of the book is consecrated to the applications of the convex duality theory in the field of monotone operators.

Keywords

Conjugate Duality Convex Optimization Regularity Conditions Subdifferential Calculus Theory of Monotone Operators calculus optimization

Authors and affiliations

  • Radu Ioan Bot
    • 1
  1. 1.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-04900-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-04899-9
  • Online ISBN 978-3-642-04900-2
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site