On Optimal Properties of Special Nonlinear and Semi-infinite Problems Arising in Parametric Optimization

Abstract

We consider a special Nonlinear Programming problem depending on integer parameters. For some values of these parameters (the ``right'' ones), this problem satisfies certain properties used in study of differential properties of optimal solutions in parametric Semi-Infinite Programming. We deduce the conditions guaranteing the existence of the ``right'' parameters values, and propose an algorithm for their determination. The conditions and the algorithm are essentially based on properties of a related linear-quadratic semi-infinite problem.