Second-Order Optimality Conditions for Problems with Locally Lipschitz Data via Tangential Directions

摘要

The goal of this article is to give some second-order necessary conditions of optimality for a constrained mathematical programming problem with locally Lipschitz data in terms of the quasi-interior directions to the constrained set at the extremum point, with the aid of Clarke's generalized derivative and Pales and Zeidan's second-order directional derivative. Sufficient optimality conditions are given too via the contingent cone. Illustrative examples are presented.