A MINIMAX APPROACH TO CHARACTERIZE QUASI ε-PARETO SOLUTIONS IN MULTIOBJECTIVE OPTIMIZATION PROBLEMS

This paper focuses on the study of optimality conditions (both necessary and sufficient) for a weakly quasi epsilon-Pareto solution to a multiobjective optimization problem by using a minimax programming approach. To establish necessary conditions for approximate solutions of minimax programming problems under a suitable constraint qualification, we use some advanced tools of variational analysis and generalized differentiation. Sufficient conditions for such solutions to the considered problem are also provided by using generalized convex functions defined in terms of the limiting subdifferential for locally Lipschitz functions. In addition, some duality results for minimax programming problems are also provided.