Abstract
In this paper, some properties of the interior of positive dual cones are discussed. With the help of dilating cones, a new notion of inner superefficient points for a set is introduced. Under the assumption of near cone-subconvexlikeness, by applying the separation theorem for convex sets, the relationship between inner superefficient points and superefficient points is established. Compared to other approximate points in the literature, inner superefficient points in this paper are really ‘approximate’.
Highlights
1 Introduction The approximate efficient solution is an important notion of vector optimization theory
Hu and Ling [ ] studied the connectedness of the cone superefficient point set in locally convex topological vector spaces
With variable ordering, we introduce the concept of inner superefficient point
Summary
The approximate efficient solution is an important notion of vector optimization theory. Loridan [ , ] introduced the concept of -solutions in general vector optimization problems. Rong and Wu [ ] considered cone-subconvexlike vector optimization problems with set-valued maps in general spaces and derived scalarization results, -saddle point theorems, and duality assertions using -Lagrangian multipliers.
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