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

Abstract

We consider a special nonlinear Programming problem depend-ing 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 paramet-ric Semi-Infinite Programming. We deduce the conditions guaran-teeing the existence of the «right» parameters values, and pro-pose an algorithm for their determination. The conditions and the algorithm are essentially based on properties of a related linear-quadratic semi-infinite problem.