Optimality Conditions in Quasidifferentiable Vector Optimization

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.