Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/4761
Title: A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems
Authors: Sun, J
Sun, D
Qi, L 
Issue Date: 2004
Source: SIAM journal on optimization, 2004, v. 14, no. 3, p. 783-806
Abstract: We study a smoothing Newton method for solving a nonsmooth matrix equation that includes semidefinite programming and the semidefinite complementarity problem as special cases. This method, if specialized for solving semidefinite programs, needs to solve only one linear system per iteration and achieves quadratic convergence under strict complementarity and nondegeneracy. We also establish quadratic convergence of this method applied to the semidefinite complementarity problem under the assumption that the Jacobian of the problem is positive definite on the affine hull of the critical cone at the solution. These results are based on the strong semismoothness and complete characterization of the B-subdifferential of a corresponding squared smoothing matrix function, which are of general theoretical interest.
Keywords: Matrix equations
Newton’s method
Nonsmooth optimization
Semidefinite complementarity problem
Semidefinite programming
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM journal on optimization 
ISSN: 1052-6234
EISSN: 1095-7189
DOI: 10.1137/S1052623400379620
Rights: © 2004 Society for Industrial and Applied Mathematics
Appears in Collections:Journal/Magazine Article

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