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Title: A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems
Authors: Sun, Jie
Sun, Defeng
Qi, Liqun
Subjects: Matrix equations
Newton’s method
Nonsmooth optimization
Semidefinite complementarity problem
Semidefinite programming
Issue Date: 2004
Publisher: Society for Industrial and Applied Mathematics
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.
Rights: © 2004 Society for Industrial and Applied Mathematics
Type: Journal/Magazine Article
DOI: 10.1137/S1052623400379620
ISSN: 1052-6234 (print)
1095-7189 (online)
Appears in Collections:AMA Journal/Magazine Articles

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