This paper is a counterpart of Bi et al., 2011. For a locally optimal solution to the nonlinear second-order cone programming (SOCP), specifically, under Robinson’s constraint qualification, we establish the equivalence among the following three conditions: the nonsingularity of Clarke’s Jacobian of Fischer-Burmeister (FB) nonsmooth system for the Karush-Kuhn-Tucker conditions, the strong second-order sufficient condition and constraint nondegeneracy, and the strong regularity of the Karush-Kuhn-Tucker point.
"Nonsingularity Conditions for FB System of Reformulating Nonlinear Second-Order Cone Programming." Abstr. Appl. Anal. 2013 1 - 21, 2013. https://doi.org/10.1155/2013/602735