Minimax programming as a tool for studying robust multi-objective optimization problems

This paper aims to investigate optimality conditions for a weakly Pareto solution to a robust multi-objective optimization problem with locally Lipschitzian data. We do this by using a minimax programming approach , namely, by establishing the necessary optimality condition for a (local) optimal solution to a robust minimax optimization problem under a suitable constraint qualification, we then employ it to arrive in the desired target. In addition, some duality results for both robust minimax optimization problems and robust multi-objective optimization problems are also provided.