Abstract

Via perturbational approach, we give an alternative dual problem for a general infinite dimensional optimization primal one, by means of a conjugation scheme based on generalized convex conjugation theory, rather than the classical Fenchel conjugation. Two sufficient regularity conditions for strong duality are stated, where the evenly convexity of the perturbation function plays a fundamental role. One of these conditions has been obtained due to the relationship between evenly convexity and cs-closedness, allowing us also to derive new properties for evenly convex sets and functions. The regularity conditions in the general setting are applied to the Fenchel primal-dual problem, and a comparison between them and an already existing closedness-type regularity condition for Fenchel duality is studied.

Author information

Contact details are reproduced from the original publication and may be historical.

Maria Dolores Fajardo

Dept. of Statistics and Operational Research, Faculty of Sciences, University of Alicante, 03080 Alicante, Spain

md.fajardo@ua.es

Keywords

  • Evenly convex function
  • generalized convex conjugation
  • Fenchel dual problem

Mathematics Subject Classification

52A20, 26B25, 90C25

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Suggested citation

M. D. Fajardo. “Regularity Conditions for Strong Duality in Evenly Convex Optimization Problems. An Application to Fenchel Duality.” Journal of Convex Analysis 22 (2015), No. 3, 711–731. https://doi.org/10.68381/jca22036

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Published by Heldermann Verlag, 2015. Rights now held by Banach Press LLC.