On the upper Lipschitz property of the KKT ... - Optimization Online
On the upper Lipschitz property of the KKT mapping for nonlinear semidefinite optimization∗ Yule Zhang†, Liwei Zhang‡ July 9, 2015
Abstract. In this note, we prove that the KKT mapping for nonlinear semidefinite optimization problem is upper Lipschitz continuous at the KKT point, under the second-order sufficient optimality conditions and the strict Robinson constraint qualification. Key words. KKT mapping, semidefinite optimization problem, upper Lipschitz continuity, second-order optimality conditions, the strict Robinson constraint qualification. AMS Subject Classifications(2000): 90C30.
1
Introduction
Let us consider the nonlinear semidefinite optimization problem of the form min f (x) s.t. h(x) = 0, g(x) ≤ 0, G(x) 0,
(1.1)
where f :
Abstract. In this note, we prove that the KKT mapping for nonlinear semidefinite optimization problem is upper Lipschitz continuous at the KKT point, under the second-order sufficient optimality conditions and the strict Robinson constraint qualification. Key words. KKT mapping, semidefinite optimization problem, upper Lipschitz continuity, second-order optimality conditions, the strict Robinson constraint qualification. AMS Subject Classifications(2000): 90C30.
1
Introduction
Let us consider the nonlinear semidefinite optimization problem of the form min f (x) s.t. h(x) = 0, g(x) ≤ 0, G(x) 0,
(1.1)
where f :
