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Necessary and Sufficient Conditions for Strong Fenchel–Lagrange Duality via a Coupling Conjugation Scheme

  • M. D. FajardoEmail author
  • J. Vidal
Article
  • 191 Downloads

Abstract

Given a general primal problem and its Fenchel–Lagrange dual one, which is obtained by using a conjugation scheme based on coupling functions and the perturbational approach, the aim in this work is to establish conditions under which strong duality can be guaranteed. To this purpose, even convexity and properness are a compulsory requirement over the involved functions in the primal problem. Furthermore, two closedness-type regularity conditions and a characterization for strong duality are derived.

Keywords

Evenly convex function Generalized convex conjugation Fenchel–Lagrange dual problem Regularity condition 

Mathematics Subject Classification

52A20 26B25 90C25 

Notes

Acknowledgements

This research was partially supported by MINECO of Spain and ERDF of EU, Grant MTM2014-59179-C2-1-P and by Consellería de Educación de la Generalitat Valenciana, Spain, Pre-doc Program Vali+d, DOCV 6791/07.06.2012, Grant ACIF-2013-156. The authors wish to thank anonymous referee for her/his valuable comments and suggestions that have significantly improved the quality of the paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.University of AlicanteAlicanteSpain
  2. 2.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany

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