Subspace of immobile indices in study of convex semidefinite problems

Abstract

We are concerned with convex problems of infinite optimization, namely a linear problem of Semidefinite Programming (SDP). For this problem, we introduce a subspace of immobile indices, prove that in the case when the Slater condition is not satisfied, this subspace is not vanishing, and suggest an algorithm that constructs a base of this subspace. We show that the subspace of immobile indices is an important characteristic of the feasible set that can be successfully used for formulation of efficient optimality conditions. These conditions do not use any constraint qualifications and therefore can be applied to wide classes of SDP problems. 1. Introduction. In the