Modified Lagrangian duality for the supremum of convex functions
Miguel Angel Goberna, Marco A. López, Michel Volle · HAL (Le Centre pour la Communication Scientifique Directe) · 2017
In this paper we associate with the problem (P) consisting of minimizing the supremum h of a family of extended real-valued convex functions on a given closed convex set C a modified Lagrange dual problem (D). Exploiting recent developments of the authors on convex duality, we provide min-sup and inf-max duality theorems for the pair (P)-(D), characterize the subdifferentials of the objective function g of the reformulation of (P) as an unconstrained problem (nothing else than the sum of h with the indicator of C) and its conjugate g^{?}, and give an explicit expression for the optimal set of (P).