TY - JOUR
T1 - A smoothing conjugate gradient method for solving systems of nonsmooth equations
AU - Narushima, Yasushi
N1 - Funding Information:
The author would like to express appreciation to Dr. Hideho Ogasawara of Tokyo University of Science for his valuable comments to accomplish this paper. The author is supported in part by the Grant-in-Aid for Scientific Research (C) 21510164 of Japan Society for the Promotion of Science.
Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2013
Y1 - 2013
N2 - Many problems in real world are reduced to systems of nonsmooth equations and hence many researchers study numerical methods for solving systems of nonsmooth equations. As numerical methods for solving systems of nonsmooth equations, Newton-like methods are known as efficient numerical methods. However, these methods are not necessarily applied directly to large-scale problems, because these methods need to store matrices. In this paper, we propose a smoothing method which is based on the nonlinear conjugate gradient method and does not store any matrices for solving systems of nonsmooth equations. In addition, we prove the global convergence property of the proposed method under standard assumptions. Finally, we give some preliminary numerical results.
AB - Many problems in real world are reduced to systems of nonsmooth equations and hence many researchers study numerical methods for solving systems of nonsmooth equations. As numerical methods for solving systems of nonsmooth equations, Newton-like methods are known as efficient numerical methods. However, these methods are not necessarily applied directly to large-scale problems, because these methods need to store matrices. In this paper, we propose a smoothing method which is based on the nonlinear conjugate gradient method and does not store any matrices for solving systems of nonsmooth equations. In addition, we prove the global convergence property of the proposed method under standard assumptions. Finally, we give some preliminary numerical results.
KW - Conjugate gradient method
KW - Global convergence
KW - Smoothing method
KW - Systems of nonsmooth equations
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U2 - 10.1016/j.amc.2013.02.060
DO - 10.1016/j.amc.2013.02.060
M3 - Article
AN - SCOPUS:84876130423
SN - 0096-3003
VL - 219
SP - 8646
EP - 8655
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 16
ER -