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Lagrange Duality for Evenly Convex Optimization Problems

Author

Listed:
  • María D. Fajardo

    (University of Alicante)

  • Margarita M. L. Rodríguez

    (University of Alicante)

  • José Vidal

    (University of Alicante)

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.

Suggested Citation

  • María D. Fajardo & Margarita M. L. Rodríguez & José Vidal, 2016. "Lagrange Duality for Evenly Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 109-128, January.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:1:d:10.1007_s10957-015-0775-z
    DOI: 10.1007/s10957-015-0775-z
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    References listed on IDEAS

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    1. Goberna, Miguel A. & Rodri'guez, Margarita M.L., 2006. "Analyzing linear systems containing strict inequalities via evenly convex hulls," European Journal of Operational Research, Elsevier, vol. 169(3), pages 1079-1095, March.
    2. Jean-Paul Penot, 2013. "Variational Analysis for the Consumer Theory," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 769-794, December.
    3. M. Fajardo & J. Vicente-Pérez & M. Rodríguez, 2012. "Infimal convolution, c-subdifferentiability, and Fenchel duality in evenly convex optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 375-396, July.
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    Cited by:

    1. M. D. Fajardo & J. Vidal, 2018. "Necessary and Sufficient Conditions for Strong Fenchel–Lagrange Duality via a Coupling Conjugation Scheme," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 57-73, January.

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