@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",
}