A note on lower semicontinuity of minimal points
Continuous behavior of minimal point sets under perturbations is a central problem in stability and sensitivity analysis of vector optimization problems. The questions of upper and/or lower semicontinuity of minimal points arise also in investigation of some other problems, for instance, in vector variational inequalities, duality theory etc. In ifinite-dimencional spaces, the main assumption which allows proving lower semicontinuity of minimal points under perturbations is the density of properly minimal points in the set of minimal points. The same remains true in any topological vector space with the notion of proper minimality suitable defined. In section 3 the author introduces the notion of strictly minimal points. In normed spaces, strict minimality generalizes the notion of supper efficiency. The main result is stated in section 4, where the key requirement is the density of strictly minimal points in the set of minimal points.
scientific article; zbMATH DE number 1788011
scientific article