Nondegenerate necessary conditions of optimality for problems without normality assumptions

Nondegenerate second-order necessary conditions of optimality for general nonlinear optimization problems are presented and discussed in this article. Besides functional equality and inequality constraints, we also consider constraints in the form of an inclusion into a given closed set. Without assuming a priori normality, our conditions remain informative for abnormal points, and, under very general assumptions also take into account the second order effect of the curvature of the set in the inclusion constraints. © 2005 IEEE.