Equivalent Conditions for Jacobian Nonsingularity in Linear Symmetric Cone Programming

In this paper we consider the linear symmetric cone programming (SCP). At a KarushKuhn-Tucker (KKT) point of SCP, we present the important equivalent conditions for 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 (2008), pp. 370-396].

• Type: Journal
• Year: 2011
• Where: JOTA
• Authors: Lingchen Kong, Levent Tunçel, Naihua Xiu
• Keywords: Dual Constraint Nondegeneracy, Important Equivalent Conditions, JOTA 2011, Linear Symmetric Cone