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Nonsingularity conditions for FB system of reformulating nonlinear second-order cone programming. (English) Zbl 1272.90047

Summary: This paper is a counterpart of [S. Bi et al., SIAM J. Optim. 21, No. 4, 1392-1417 (2011; Zbl 1246.90114)]. 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.

MSC:

90C22 Semidefinite programming
90C30 Nonlinear programming

Citations:

Zbl 1246.90114
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References:

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