Necessary and sufficient conditions for the efficient solutions of nondifferentiable multiobjective problems

The necessary conditions for the efficient solutions of multiobjective problems with locally Lipschitz objective and constraint functions are presented. Under the assumption of convexity, these conditions are also sufficient conditions. For its application, the optimality conditions for the multiobjective problems including extremal-value functions are obtained. The necessary conditions are derived by means of the generalized Motzkin´s lemma and are expressed in terms of Clarke´s generalized gradients (1975).