Infimal convolution, c-subdifferentiability, and Fenchel duality in evenly convex optimization

• M.D. Fajardo ^[1] ; J. Vicente-Pérez ^[1] ; M.M.L. Rodríguez ^[1]
  1. [1] Universitat d'Alacant

     Universitat d'Alacant

     Alicante, España

     
• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 20, Nº. 2, 2012, págs. 375-396
• Idioma: inglés
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• Resumen

  • In this paper we deal with strong Fenchel duality for infinite-dimensional optimization problems where both feasible set and objective function are evenly convex. To this aim, via perturbation approach, a conjugation scheme for evenly convex functions, based on generalized convex conjugation, is used. The key is to extend some well-known results from convex analysis, involving the sum of the epigraphs of two conjugate functions, the infimal convolution and the sum formula of ε-subdifferentials for lower semicontinuous convex functions, to this more general framework.