On study of properties of special nonlinear problems arising in parametric SIP

Abstract

We study parametric Semi-infinite Programming (SIP) problems with finitely representable compact index sets and investigate dependence of solutions of these problems on the parameters. We show that differential properties of solutions of the arametric SIP problems can be formulated in terms of solutions of some special auxiliary Nonlinear Programming (NLP) problems depending on a finite number of integers (parameters). We discover different properties of solutions of these NLP problems w.r.t. the values of the integers that permit us to obtain important conclusions about behavior of solution.