Local structure of feasible sets in nonlinear programming, part II: Nondegeneracy

Abstract

In this paper we examine the local structure of the feasible set of a nonlinear programming problem under the condition of nondegeneracy. We introduce this condition, examine its relationships to known properties of optimization problems, and show that when it holds at a given point the portion of the feasible set near that point is diffeomorphic to a simple convex set (often polyhedral). Moreover, this diffeomorphic relation is stable under small changes in the problem functions.

Sponsored by the U.S. National Science Foundation under Grant No. MCS 8200632. Preliminary research for this paper was done at the Centre de Recherche de Mathématiques de la Décision, Université Paris-IX Dauphine, with travel support from C.N.R.S., and the writing was completed at the International Institute for Applied Systems Analysis, Laxenburg, Austria. The author thanks all of these agencies for their support of this work.