Existence and stability to vector optimization problems via improvement sets

In this paper, we consider vector optimization problems via improvement sets and investigate their existence and the stability.More precisely, we introduce Benson weakly efficient solutions for nonconvex vector optimization problems and investigate the existence of the solution via the scalarization method.Based on generalized convexlikeness and relaxed continuity properties of mappings, we formulate sufficient conditions of the (semi) continuity for solution mappings of parametric vector optimization problems.As an application, we investigate the special case of co-radiant vector optimization problems.