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SIAMJO
2008

Constraint Nondegeneracy, Strong Regularity, and Nonsingularity in Semidefinite Programming

11 years 5 months ago
Constraint Nondegeneracy, Strong Regularity, and Nonsingularity in Semidefinite Programming
It is known that the Karush-Kuhn-Tucker (KKT) conditions of semidefinite programming can be reformulated as a nonsmooth system via the metric projector over the cone of symmetric and positive semidefinite matrices. We show in this paper that the primal and dual constraint nondegeneracies, the strong regularity, the nonsingularity of the B-subdifferential of this nonsmooth system, and the nonsingularity of the corresponding Clarke's generalized Jacobian, at a KKT point are all equivalent. Moreover, we prove the equivalence between each of these conditions and the nonsingularity of Clarke's generalized Jacobian of the smoothed counterpart of this nonsmooth system used in several globally convergent smoothing Newton methods. In particular, we establish the quadratic convergence of these methods under the primal and dual constraint nondegeneracies, but without the strict complementarity. Key words: Semidefinite programming, constraint nondegeneracy, strong regularity, nonsingula...
Zi Xian Chan, Defeng Sun
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2008
Where SIAMJO
Authors Zi Xian Chan, Defeng Sun
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