| Article ID: | iaor20112651 |
| Volume: | 148 |
| Issue: | 2 |
| Start Page Number: | 364 |
| End Page Number: | 389 |
| Publication Date: | Feb 2011 |
| Journal: | Journal of Optimization Theory and Applications |
| Authors: | Tunel Levent, Kong Lingchen, Xiu Naihua |
| Keywords: | Programming (cone), KarushKuhnTucker (KKT) |
In this paper we consider the linear symmetric cone programming (SCP). At a Karush‐Kuhn‐Tucker (KKT) point of SCP, we present the important conditions equivalent to the nonsingularity of Clarke’s generalized Jacobian of the KKT nonsmooth system, such as primal and dual constraint nondegeneracy, the strong regularity, and the nonsingularity of the B‐subdifferential of the KKT system. This affirmatively answers an open question by Chan and Sun (SIAM J. Optim. 19:370–396, 2008).