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

Top - 2011
M. D. Fajardo1, J. Vicente-Pérez1, M. M. L. Rodríguez1
1Department of Statistics and Operations Research, University of Alicante, Alicante, Spain

Tóm tắt

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.

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