Optimality Conditions in Quasidifferentiable Vector Optimization
Tadeusz Antczak · Journal of Optimization Theory and Applications · 2016
In the paper, the quasidifferentiable vector optimization problem with the inequality constraints is considered. The Fritz John-type necessary optimality conditions and the Karush–Kuhn–Tucker-type necessary optimality conditions for a weak Pareto solution are derived for such a nonsmooth vector optimization problem. Further, the concept of an F -convex function with respect to a convex compact set is introduced. Then, the sufficient optimality conditions for a (weak) Pareto optimality of a feasible solution are established for the considered nonsmooth multiobjective optimization problem under assumptions that the involved functions are quasidifferentiable F -convex with respect to convex compact sets which are equal to Minkowski sum of their subdifferentials and superdifferentials at this point.