About one discrete analog of Hausdorff semi-continuity of suitable mapping in a vector combinatorial problem with a parametric principle of optimality ("from Slater to lexicographic")

Abstract

multicriteria linear combinatorial problem is considered, principle of optimality of which is defined by a partitioning of partial criteria onto groups with Slater preference relation within each group and the lexicographic preference relation between them. Quasistability of the problem is investigated. This type of stability is a discrete analog of Hausdorff lower semicontinuity of the many-valued mapping that defines the choice function. A formula of quasistability radius is derived for the case of metric \(l_\infty.\) Some conditions of quasistability are stated as corollaries.

Keywords

• vector optimization
• set of weak Slater optima
• set of lexicographically optimal trajectories
• quasistability
• quasistability radius