On a special nonlinear problem arising in the study of convex SIP problems - Kostyukova, O. I. (2012)
We continue a study of convex problems of Semi-In¯nite Programming (SIP) started in [6, 7]. In the Implicit Optimality Criterion from [6], we formulated the optimality conditions for convex SIP problem in terms of such the conditions for a special Nonlinear Programming (NLP) problem. In the present paper, we study some speci¯c properties of this nonlinear problem and obtain e±cient optimality conditions for it. We show that in the case when the constraint function of the initial SIP problem is analytical, the optimality conditions take the form of criterion.