Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps

In this paper, by using the notion of strong subdifferential and epsilon-subdifferential, necessary optimality conditions are established firstly for an epsilon-weak Pareto minimal point and an epsilon-proper Pareto minimal point of a vector optimization problem, where its objective function and constraint set are denoted by using differences of two vector-valued maps, respectively. Then, by using the concept of approximate pseudo-dissipativity, sufficient optimality conditions are obtained. As an application of these results, sufficient and necessary optimality conditions are also given for an epsilon-weak Pareto minimal point and an epsilon-proper Pareto minimal point of a vector fractional mathematical programming.