On Second-Order Sufficient Conditions in Constrained Nonsmooth Optimization

Abstract

In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called $ℓ$-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednařík and K. Pastor, Math. Program. Ser. A, 113(2008), 283–298] to constrained optimization problems.