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A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate
×÷Õß:Sun, M (Sun, Min)[ 1 ] ; Liu, J (Liu, Jing)[ 2 ]
ABSTRACT AND APPLIED ANALYSIS
ÎÄÏ׺Å: 386030
DOI: 10.1155/2014/386030
³ö°æÄê: 2014
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A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribiere-Polyak) conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor.. is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.
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KeyWords Plus:NONLINEAR MONOTONE EQUATIONS; GRADIENT PROJECTION METHOD; CONVEX CONSTRAINTS; SYSTEMS; ALGORITHM
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ͨѶ×÷ÕßµØÖ·: Sun, M (ͨѶ×÷Õß)
Zaozhuang Univ, Sch Math & Stat, Zaozhuang City 277160, Shandong, Peoples R China.
µØÖ·:
[ 1 ] Zaozhuang Univ, Sch Math & Stat, Zaozhuang City 277160, Shandong, Peoples R China
[ 2 ] Zhejiang Univ Finance & Econ, Sch Math & Stat, Hangzhou 310018, Zhejiang, Peoples R China
µç×ÓÓʼþµØÖ·:ziyouxiaodou@163.com
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Nature Science Foundation of Shandong Province
ZR2012AL08
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HINDAWI PUBLISHING CORPORATION, 410 PARK AVENUE, 15TH FLOOR, #287 PMB, NEW YORK, NY 10022 USA
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Ñо¿·½Ïò:Mathematics
Web of Science Àà±ð:Mathematics, Applied; Mathematics
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ÎÄÏ×ÀàÐÍ:Article
ÓïÖÖ:English
Èë²ØºÅ: WOS:000336580700001
ISSN: 1085-3375
µç×Ó ISSN: 1687-0409
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Impact Factor (Ó°ÏìÒò×Ó): Journal Citation Reports®
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IDS ºÅ: AI0ZZ
Web of Science ºËÐĺϼ¯ÖÐµÄ "ÒýÓõIJο¼ÎÄÏ×": 15
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