Levenberg-marquardt method for absolute value equation associated with second-order cone

Xin He Miao; Kai Yao; Ching Yu Yang; Jein Shan Chen

doi:10.3934/naco.2021050

Levenberg-marquardt method for absolute value equation associated with second-order cone

Xin He Miao, Kai Yao, Ching Yu Yang, Jein Shan Chen^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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 stan-dard 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 indi-cates that the proposed algorithm could also be a good choice for solving the SOCAVE.

Original language	English
Pages (from-to)	47-61
Number of pages	15
Journal	Numerical Algebra, Control and Optimization
Volume	12
Issue number	1
DOIs	https://doi.org/10.3934/naco.2021050
Publication status	Published - 2022 Mar

Keywords

Absolute value equations
Armijo line search
Levenberg-Marquardt algorithm
Second-order cone

ASJC Scopus subject areas

Algebra and Number Theory
Control and Optimization
Applied Mathematics

Access to Document

10.3934/naco.2021050

Cite this

@article{6c0a770c8d0543bca34a7433c577acaf,

title = "Levenberg-marquardt method for absolute value equation associated with second-order cone",

abstract = "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 stan-dard 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 indi-cates that the proposed algorithm could also be a good choice for solving the SOCAVE.",

keywords = "Absolute value equations, Armijo line search, Levenberg-Marquardt algorithm, Second-order cone",

author = "Miao, {Xin He} and Kai Yao and Yang, {Ching Yu} and Chen, {Jein Shan}",

note = "Funding Information: 2020 Mathematics Subject Classification. Primary: 26B05, 65K10; Secondary: 26B35, 90C33. Key words and phrases. Second-order cone, Absolute value equations, Levenberg-Marquardt algorithm, Armijo line search. The first author is supported by by National Natural Science Foundation of China (No. 11471241) and Natural Science Foundation of Inner Mongolia (No. 2019LH01001). The last author is supported by Ministry of Science and Technology, Taiwan. ∗ Corresponding author: Jein-Shan Chen. Publisher Copyright: {\textcopyright} 2022, American Institute of Mathematical Sciences. All rights reserved.",

year = "2022",

month = mar,

doi = "10.3934/naco.2021050",

language = "English",

volume = "12",

pages = "47--61",

journal = "Numerical Algebra, Control and Optimization",

issn = "2155-3289",

publisher = "American Institute of Mathematical Sciences",

number = "1",

}

TY - JOUR

T1 - Levenberg-marquardt method for absolute value equation associated with second-order cone

AU - Miao, Xin He

AU - Yao, Kai

AU - Yang, Ching Yu

AU - Chen, Jein Shan

N1 - Funding Information: 2020 Mathematics Subject Classification. Primary: 26B05, 65K10; Secondary: 26B35, 90C33. Key words and phrases. Second-order cone, Absolute value equations, Levenberg-Marquardt algorithm, Armijo line search. The first author is supported by by National Natural Science Foundation of China (No. 11471241) and Natural Science Foundation of Inner Mongolia (No. 2019LH01001). The last author is supported by Ministry of Science and Technology, Taiwan. ∗ Corresponding author: Jein-Shan Chen. Publisher Copyright: © 2022, American Institute of Mathematical Sciences. All rights reserved.

PY - 2022/3

Y1 - 2022/3

N2 - 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 stan-dard 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 indi-cates that the proposed algorithm could also be a good choice for solving the SOCAVE.

AB - 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 stan-dard 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 indi-cates that the proposed algorithm could also be a good choice for solving the SOCAVE.

KW - Absolute value equations

KW - Armijo line search

KW - Levenberg-Marquardt algorithm

KW - Second-order cone

UR - http://www.scopus.com/inward/record.url?scp=85121985446&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85121985446&partnerID=8YFLogxK

U2 - 10.3934/naco.2021050

DO - 10.3934/naco.2021050

M3 - Article

AN - SCOPUS:85121985446

SN - 2155-3289

VL - 12

SP - 47

EP - 61

JO - Numerical Algebra, Control and Optimization

JF - Numerical Algebra, Control and Optimization

IS - 1

ER -

Levenberg-marquardt method for absolute value equation associated with second-order cone

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this