Inverse optimization in semi-infinite linear programs

Abstract

Given the costs and a feasible solution for a finite-dimensional linear program (LP), inverse optimization involves finding new costs that are close to the original ones and render the given solution optimal. Ahuja and Orlin employed the absolute weighted sum metric to quantify distances between costs, and then applied duality to establish that inverse optimization reduces to another finite-dimensional LP. This paper extends this to semi-infinite linear programs (SILPs). A convergent Simplex algorithm to tackle the inverse SILP is proposed.