On the Density of Henig Efficient Points in Locally Convex Topological Vector Spaces

Weak Henig proper solution sets for set optimization problems

“…The first aim of this paper is to derive some properties of the Henig dilating cone and establish the continuity of nonlinear scalarizing functions with respect to the Henig dilating cone. In the past decades, density theorems for various proper efficiency, especially the generalizations of the density theorem of Arrow, Barankin and Blackwell have been extensively studied in the literature (see, e.g., [13][14][15][16][17][18][19][20][21][22][23][24][25] and the references therein). Up to our knowledge, the set of Henig proper efficient points is dense in the set of efficient points under some suitable conditions (see, e.g., [4,17,18,21,23,25]).…”

“…In the past decades, density theorems for various proper efficiency, especially the generalizations of the density theorem of Arrow, Barankin and Blackwell have been extensively studied in the literature (see, e.g., [13][14][15][16][17][18][19][20][21][22][23][24][25] and the references therein). Up to our knowledge, the set of Henig proper efficient points is dense in the set of efficient points under some suitable conditions (see, e.g., [4,17,18,21,23,25]). Thus, it is natural to understand whether we can obtain that weak Henig proper solution set for set optimization problems is dense in minimal solution set for set optimization problems.…”