New duality results for evenly convex optimization problems. (2nd September 2021) - Fajardo, M. D.; Grad, S. M.; Vidal, J.
ABSTRACT: We present new results on optimization problems where the involved functions are evenly convex. By means of a generalized conjugation scheme and the perturbation theory introduced by Rockafellar, we propose an alternative dual problem for a general optimization one defined on a separated locally convex topological space. Sufficient conditions for converse and total duality involving the even convexity of the perturbation function and c -subdifferentials are given. Formulae for the c -subdifferential and biconjugate of the objective function of a general optimization problem are provided, too. We also characterize the total duality by means of the saddle-point theory for a notion of Lagrangian adapted to the considered framework.