Optimality conditions and sensitivity analysis in parametric convex minimax programming

In this paper, we study optimality conditions as well as sensitivity analysis of parametric convex minimax programming problems. The main tools used here are the formulas for computing the subdifferentials of maximum functions under some suitable regularity conditions. More precisely, we use these tools to study optimality conditions for the problem under consideration. These results are then applied to obtain optimality conditions for multiobjective optimization problems, which constitute the first part of the paper. In the second part, we derive formulas for computing the subdifferential in the sense of convex analysis and singular subdifferential of the optimal value function for the problem in question.