Journal of Optimization Theory and Applications

, Volume 148, Issue 2, pp 364–389 | Cite as

Equivalent Conditions for Jacobian Nonsingularity in Linear Symmetric Cone Programming

  • Lingchen Kong
  • Levent Tunçel
  • Naihua Xiu


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).


Linear symmetric cone programming Nonsingularity Constraint nondegeneracy Strong regularity Variational analysis 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Applied MathematicsBeijing Jiaotong UniversityBeijingP.R. China
  2. 2.Department of Combinatorics and Optimization, Faculty of MathematicsUniversity of WaterlooWaterlooCanada

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