Evaluation of the epi-convergence

Abstract

The paper presents an equivalent characterization of the epi-convergence of lower semicontinuous functions. The proposed ‘measures’ naturally estimate the distance between optimal values of two optimization programs. A comparison of optimal solutions is more complex. We propose an estimation for a given function which can be taken as the excess of a set over another, being in metric space. Hence, we receive an estimate of the distance between optimal solutions.