Some Pareto optimality results for nonsmooth multiobjective optimization problems with equilibrium constraints

In this paper, we study the nonsmooth multiobjective optimization problems with equilibrium constraints (MOMPEC). First, we extend the Guignard constraint qualification for MOMPEC, and then more constraint qualifications are developed. Also, the relationships between them are investigated. Moreover, we introduce the notion of primal Pareto stationarity and some dual Pareto stationarity concepts for a feasible point of MOMPEC. Some necessary optimality conditions are derived for any Pareto optimality solution of MOMPEC under weak assumptions. Indeed, we just need the objective functions to be locally Lipschitz. Further, we indicate our defined Pareto stationarity concepts are also sufficient conditions under the generalized convexity requirements.