Error bounds for the inverse feasible set mapping in linear semi-infinite optimization via a sensitivity dual approach

Abstract

In this article, some sensitivity analysis of the dual optimal value in linear semi-infinite optimization is carried out via the notion of primal/dual asymptotic solution. The sensitivity results are then applied to derive some Hoffman-type inequalities (error bounds). Like in [Renegar, J., 1994, Some perturbation theory for linear programming. Mathematical Programming, 65A, 73–91], asymptotic solutions also turn out to be a key tool for any sensitivity analysis in the setting of semi-infinite linear duality.