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Lagrange Duality for Evenly Convex Optimization Problems

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Abstract

An evenly convex function on a locally convex space is an extended real-valued function, whose epigraph is the intersection of a family of open halfspaces. In this paper, we consider an infinite-dimensional optimization problem, for which both objective function and constraints are evenly convex, and we recover the classical Lagrange dual problem for it, via perturbational approach. The aim of the paper was to establish regularity conditions for strong duality between both problems, formulated in terms of even convexity.

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Acknowledgments

This research was partially supported by MINECO of Spain, Grant MTM2011-29064-C03-02 and by Consellería d’Educació 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 referees for their valuable comments and suggestions that have significantly improved the quality of the paper.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, University of Alicante, 03080, Alicante, Spain

    María D. Fajardo, Margarita M. L. Rodríguez & José Vidal

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  1. María D. Fajardo
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  2. Margarita M. L. Rodríguez
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  3. José Vidal
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Correspondence to María D. Fajardo.

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Fajardo, M.D., Rodríguez, M.M.L. & Vidal, J. Lagrange Duality for Evenly Convex Optimization Problems. J Optim Theory Appl 168, 109–128 (2016). https://doi.org/10.1007/s10957-015-0775-z

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  • DOI: https://doi.org/10.1007/s10957-015-0775-z

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