CHARACTERIZATION OF THE ROBUST ISOLATED CALMNESS FOR A CLASS OF CONIC PROGRAMMING PROBLEMS

Indexed by:Journal Article

Date of Publication:2017-01-01

Journal:SIAM JOURNAL ON OPTIMIZATION

Included Journals:Scopus、EI、SCIE

Volume:27

Issue:1

Page Number:67-90

ISSN:1052-6234

Key Words:stability; robust isolated calmness; C-2-cone reducible sets; strict Robinson constraint qualification; second order sufficient condition; Aubin property

Abstract:This paper is devoted to studying the robust isolated calmness of the Karush Kuhn Tucker (KKT) solution mapping for a large class of interesting conic programming problems (including most commonly known ones arising from applications) at a locally optimal solution. Under the Robinson constraint qualification, we show that the KKT solution mapping is robustly isolated calm if and only if both the strict Robinson constraint qualification and the second order sufficient condition hold. This implies, among others, that at a locally optimal solution the second order sufficient condition is needed for the KKT solution mapping to have the Aubin property.