Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps

A Note on the Paper “Optimality Conditions for Vector Optimization Problems with Difference of Convex Maps”

“…Let us briefly recall the notation used in this work. For the most part, we follow notations as in [8]. Throughout this paper, X is a metrizable topological vector space.…”

“…We consider the following cone-constrained vector optimization problem as in [8] sometimes called DC vector optimization where refers to difference of two cone convex functions:…”

“…The following definition is based on metrizable topological vector space which is slightly different from Definition 3.1 in [8]. We note that X with the topology generated by metric d is a topological vector space.…”

“…(Theorem 3.1 [8]) Let x ∈ Ω. Assume that the set-valued maps ∂ ǫ G and ∂S are both approximately pseudo-dissipative at x.…”

“…In [8], Guo and Li use the notions of strong subdifferential and epsilon subdifferential to obtain necessary and sufficient optimality conditions for an epsilon-weak Pareto minimal point and an epsilon-proper Pareto minimal point of a DC vector optimization problem. In this article, we show that some theorems and results in [8] are not correct. Furthermore, we clarify an existence gap by providing some counterexamples.…”