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Title: Constraint nondegeneracy, strong regularity, and nonsingularity in semidefinite programming
Authors: Chan, Z.X.
Sun, D. 
Keywords: Constraint nondegeneracy
Quadratic convergence
Semidefinite programming
Strong regularity
Variational analysis
Issue Date: 2008
Citation: Chan, Z.X., Sun, D. (2008). Constraint nondegeneracy, strong regularity, and nonsingularity in semidefinite programming. SIAM Journal on Optimization 19 (1) : 370-396. ScholarBank@NUS Repository.
Abstract: 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. © 2008 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Optimization
ISSN: 10526234
DOI: 10.1137/070681235
Appears in Collections:Staff Publications

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