Please use this identifier to cite or link to this item: https://doi.org/10.1137/S1052623400379620
Title: A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems
Authors: Sun, J. 
Sun, D. 
Liqun, Q.I.
Keywords: Matrix equations
Newton's method
Nonsmooth optimization
Semidefinite complementarity problem
Semidefinite programming
Issue Date: 2004
Source: Sun, J., Sun, D., Liqun, Q.I. (2004). A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems. SIAM Journal on Optimization 14 (3) : 783-806. ScholarBank@NUS Repository. https://doi.org/10.1137/S1052623400379620
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.
Source Title: SIAM Journal on Optimization
URI: http://scholarbank.nus.edu.sg/handle/10635/44236
ISSN: 10526234
DOI: 10.1137/S1052623400379620
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
File Description SizeFormatAccess SettingsVersion 
2004-squared_smoothing_newton_method_nonsmooth-published.pdf237.64 kBAdobe PDF

OPEN

PublishedView/Download

SCOPUSTM   
Citations

46
checked on Dec 7, 2017

WEB OF SCIENCETM
Citations

42
checked on Nov 22, 2017

Page view(s)

58
checked on Dec 10, 2017

Download(s)

10
checked on Dec 10, 2017

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.