NONDIFFERENTIABLE NONLINEAR MULTIOBJECTIVE OPTIMIZATION UNDER GENERALIZED TYPE I UNIVEXITY

In this paper, we consider a nondi erentiable nonlinear multiobjective optimization with inequality constraints. We introduce new concepts of α-dI-V-type-I and generalized α-dI-V-type-I univexity in which each component of the objective and constraint functions is directionally di erentiable in its own direction di. Some Karush-Kuhn-Tucker type sucient optimality conditions are established for a feasible point to be an ecient solution. Several Mond-Weir type duality results are also obtained under the assumptions of generalized α-dI-V-type-I univexity. Our results generalize and extend the previously known results in this area.