LEVENBERG-MARQUARDT METHOD FOR ABSOLUTE VALUE EQUATION ASSOCIATED WITH SECOND-ORDER CONE

被引：6

作者：

Miao, Xin-He ^{[1
]}

Yao, Kai ^{[1
]}

Yang, Ching-Yu ^{[2
]}

Chen, Jein-Shan ^{[2
]}

机构：

[1] Tianjin Univ, Sch Math, Tianjin 300072, Peoples R China

[2] Natl Taiwan Normal Univ, Dept Math, Taipei 11677, Taiwan

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2022年 / 12卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Second-order cone; Absolute value equations; Levenberg-Marquardt algorithm; Armijo line search; GENERALIZED NEWTON METHOD; COMPLEMENTARITY; ALGORITHM; CONVERGENCE; CONVEX;

D O I：

10.3934/naco.2021050

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we suggest the Levenberg-Marquardt method with Armijo line search for solving absolute value equations associated with the second-order cone (SOCAVE for short), which is a generalization of the standard absolute value equation frequently discussed in the literature during the past decade. We analyze the convergence of the proposed algorithm. For numerical reports, we not only show the efficiency of the proposed method, but also present numerical comparison with smoothing Newton method. It indicates that the proposed algorithm could also be a good choice for solving the SOCAVE.

引用

页码：47 / 61

页数：15

共 35 条

[1]

[Anonymous], 1995, NONLINEAR PROGRAMMIN

[2] A globally and quadratically convergent method for absolute value equations [J].

Caccetta, Louis ;

Qu, Biao ;

Zhou, Guanglu .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2011, 48 (01) :45-58

[3]

Chen J.-S., 2019, Springer Optimization and Its Applications, V143

[4] The convex and monotone functions associated with second-order cone [J].

Chen, Jein-Shan .

OPTIMIZATION, 2006, 55 (04) :363-385

[5]

Chen JS, 2012, PAC J OPTIM, V8, P33

[6] An unconstrained smooth minimization reformulation of the second-order cone complementarity problem [J].

Chen, JS ;

Tseng, P .

MATHEMATICAL PROGRAMMING, 2005, 104 (2-3) :293-327

[7] Analysis of nonsmooth vector-valued functions associated with second-order cones [J].

Chen, JS ;

Chen, X ;

Tseng, P .

MATHEMATICAL PROGRAMMING, 2004, 101 (01) :95-117

[8] Numerical Simulation of Binary Alloy Crystal growth of Multiple dendrites and Directional solidification Using Phase-field Method [J].

Chen, Ming ;

Jiang, Yu ;

Sun, Wenlong ;

Hu, Xiaodong ;

Liu, Chunli .

ADVANCED TECHNOLOGIES IN MANUFACTURING, ENGINEERING AND MATERIALS, PTS 1-3, 2013, 774-776 :703-706

[9] Unified smoothing functions for absolute value equation associated with second-order cone [J].

Chieu Thanh Nguyen ;

Saheya, B. ;

Chang, Yu-Lin ;

Chen, Jein-Shan .

APPLIED NUMERICAL MATHEMATICS, 2019, 135 :206-227

[10] Benchmarking optimization software with performance profiles [J].

Dolan, ED ;

Moré, JJ .

MATHEMATICAL PROGRAMMING, 2002, 91 (02) :201-213

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