A projection method for a system of nonlinear monotone equations with convex constraints

被引：116

作者：

Wang, Chuanwei ^{[1
]}

Wang, Yiju

Xu, Chuanliang

机构：

[1] Shandong Agr Univ, Coll Informat Sci & Engn, Shandong 271018, Peoples R China

[2] Qufu Normal Univ, Sch Operat Res & Management Sci, Shandong 276800, Peoples R China

[3] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

[4] Rizhao Vocat & Tech Coll, Shandong 276800, Peoples R China

来源：

MATHEMATICAL METHODS OF OPERATIONS RESEARCH | 2007年 / 66卷 / 01期

关键词：

nonlinear equations; global convergence; linear convergence rate; projection method; monotone mapping;

D O I：

10.1007/s00186-006-0140-y

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we propose a projection method for solving a system of nonlinear monotone equations with convex constraints. Under standard assumptions, we show the global convergence and the linear convergence rate of the proposed algorithm. Preliminary numerical experiments show that this method is efficient and promising.

引用

页码：33 / 46

页数：14

共 18 条

[1]

[Anonymous], 2001, COMPUTING SUPPLEMENT, DOI DOI 10.1007/978-3-7091-6217-0

[2] An affine scaling trust-region approach to bound-constrained nonlinear systems [J].

Bellavia, S ;

Macconi, M ;

Morini, B .

APPLIED NUMERICAL MATHEMATICS, 2003, 44 (03) :257-280

[3] PROJECTED GRADIENT METHODS FOR LINEARLY CONSTRAINED PROBLEMS [J].

CALAMAI, PH ;

MORE, JJ .

MATHEMATICAL PROGRAMMING, 1987, 39 (01) :93-116

[4]

El-Hawary ME, 1996, OPTIMAL POWER FLOW S

[5]

GABRIEL SA, 1994, LARGE SCALE OPTIMIZATION: STATE OF THE ART, P155

[6] 2-METRIC PROJECTION METHODS FOR CONSTRAINED OPTIMIZATION [J].

GAFNI, EM ;

BERTSEKAS, DP .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1984, 22 (06) :936-964

[7] A new hybrid generalized proximal point algorithm for variational inequality problems [J].

Han, D .

JOURNAL OF GLOBAL OPTIMIZATION, 2003, 26 (02) :125-140

[8] Levenberg-Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints [J].

Kanzow, C ;

Yamashita, N ;

Fukushima, T .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 172 (02) :375-397

[9] FINDING ALL SOLUTIONS OF NONLINEARLY CONSTRAINED SYSTEMS OF EQUATIONS [J].

MARANAS, CD ;

FLOUDAS, CA .

JOURNAL OF GLOBAL OPTIMIZATION, 1995, 7 (02) :143-182

[10] A new projection method for variational inequality problems [J].

Solodov, MV ;

Svaiter, BF .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (03) :765-776

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