Nonsmooth Multiobjective Problems and Generalized Vector Variational Inequalities Using Quasi-Efficiency

摘要

In this paper, a multiobjective problem with a feasible set defined by inequality, equality and set constraints is considered, where the objective and constraint functions are locally Lipschitz. Here, a generalized Stampacchia vector variational inequality is formulated as a tool to characterize quasi- or weak quasi-efficient points. By using two new classes of generalized convexity functions, under suitable constraint qualifications, the equivalence between Kuhn-Tucker vector critical points, solutions to the multiobjective problem and solutions to the generalized Stampacchia vector variational inequality in both weak and strong forms will be proved.