Abstract:

Using the idea of convexificators, we proposed constraint qualifications and studied the existence and boundedness of the Kuhn\|Tucker multipliers for a nonsmooth multiobjective optimization problem withinequality constraints and an arbitrary set constraint. We showed that in locally weak efficient solutions where the objective and constraint functions are locally Lipschitz, the constraint qualifications are necessary andsufficient conditions for the Kuhn\|Tucker multiplier sets to be nonempty and bounded.

Key words: convexificators, constraint qualifications, existence and boundedness of KuhnTucker multipliers, nonsmooth multiobjective optimization