On the classical necessary second-order optimality conditions
In this paper a nonconvex optimization problem in \({\mathbb R}^n\) with equality and inequality constraints is considered. Assuming that the Mangasarian-Fromovitz constraint qualifications hold at a local optimal solution, the aim is to provide sufficient conditions that imply the necessary second-order conditions CN2, with the same Lagrange multipliers. Two main results provide some sufficient conditions; in particular, the second one shows that CN2 holds if the dimension \(n\leq 2\) or if the number of active inequality constraints is at most two. These conditions are sharp, as proved in the counterexample given in the end of the paper.
Mangasarian-Fromovitz constraint qualifications
scientific article; zbMATH DE number 2153864
scientific article