Equivalent Conditions for Jacobian Nonsingularity in Linear Symmetric Cone Programming

@article{Kong2011EquivalentCF,
  title={Equivalent Conditions for Jacobian Nonsingularity in Linear Symmetric Cone Programming},
  author={Lingchen Kong and Levent Tunçel and Naihua Xiu},
  journal={J. Optimization Theory and Applications},
  year={2011},
  volume={148},
  pages={364-389}
}
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].