Characterizations of improvement sets via quasi interior and applications in vector optimization (Q276329)

The concept of quasi interior of a set in a real nontrivial separated locally convex topological vector space \(Y\) is introduced. Let \(E \subseteq Y\), \(E \neq \emptyset\), let \(K\) be a proper convex cone in \(Y\), \(0 \not\in E\), \(E+K = E\). Then \(E\) is said to be an improvement set with repect to \(K\). Characterizations of improvement sets via quasi interior are presented, an alternative theorem and a scalarization result of weak \(E\)-efficient solutions are established for vector optimization problems with set-valued maps. The concluding part of the paper contains numerical examples illustrating the obtained theoretical results.