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
