A note on semicontinuity of the solution mapping for parametric set optimization problems

Continuity of Solution Mappings for Parametric Set Optimization Problems under Partial Order Relations

“…for each λ ∈ Λ , K x λ = with respect to 0 0 y = . Indeed, we obtain that The following example is given to show that the m 1 -property in [25]…”

“…In this section, we shall give the comparisons between the results ( The following example is given to show that the converse m 1 -property in [25] is unnecessary in Theorem 4.1 for this paper.…”

“…Recently, Karaman [23] introduced two new order relations on family of sets called m 1 and m 2 set order relations which are partial order relations and are smaller than the vector order relations introduced in [24]. Preechasilp and Wangkeeree [25] gave some sufficient conditions for the semicontinuity of the solution mapping to a parametric set optimization problem with (converse) m 1 -property assumptions under m 1 set order relation. Since it is difficult to check the (converse) m 1 -property assumptions, this limits the applications of stability of set optimization problems (See Example 5.1 and 5.2).…”

“…The proof of Theorem 4.1 is different from one of Theorem 3.4 of Preechasilp and Wangkeeree[25]. Moreover, in Theorem 4.1, we do not use converse m 1 -property for set-valued objective mapping F, which is applied in Theorem 3.4 of Preechasilp and Wangkeeree[25]. And the order relations we used are smaller than the set less order relations in[16] [21] [22] [26].…”

Levitin–Polyak well-posedness in set optimization concerning Pareto efficiency

“…For the investigation of preferences over sets, the set criterion seems to be more natural and suitable for applications than the vector one. As a result, numerous aspects of set optimization problems and their applications have been considered in a great many publications; see, for instance, [1,2,6,9,11,14,29] and the references therein.…”