On a new approach to optimality conditions for Convex Semi-Infinite Programming
We consider convex problem of Semi-Infinite Programming (SIP) with multi - dimensional index set. In study of these problems we apply a new approach based on the notions of immobile indices and their immobility orders. We formulate the first order optimality conditions for conves SIP 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.