On the existence and the stability of solutions in nonsmooth vector optimization

Abstract: The paper is devoted to the existence of weak Pareto solutions and the weak sharp minima at infinity property for a general class of constrained nonsmooth vector optimization problems with unbounded constraint set via asymptotic cones and generalized asymptotic functions. Then we show that these conditions are useful for studying the solution stability of nonconvex vector optimization problems with linear perturbation. We also provide some applications for a subclass of nonsmooth robustly quasiconvex vector optimization problems.