Sequential Lagrange multiplier conditions for minimax programming problems

In this article, we study nonsmooth convex minimax programming problems with cone constraint and abstract constraint. Our aim is to develop sequential Lagrange multiplier rules for this class of problems in the absence of any constraint qualification. These rules are obtained in terms of ϵ–subdifferentials of the functions. As an application of these rules, a sequential dual is proposed and sequential duality results are presented.