Implicit optimality criterion for convex SIP problem with box constrained index set

Abstract

We consider a convex problem of Semi-Infinite Programming (SIP) with a multidimensional index set defined by a finite number of box constraints. In study of this problem we apply the approach suggested in Kostyukova et al. (Int. J. Math. Stat. 13(J08):13–33, 2008) for convex SIP problems with one-dimensional index sets and based on the notions of immobile indices and their immobility orders. For the problem under consideration we formulate optimality conditions that are explicit and have the form of criterion. We compare this criterion with other known optimality conditions for SIP and show its efficiency in the convex case.