• 论文 •

### 求解二阶锥绝对值方程组的非单调光滑牛顿算法

1. 1. 辽宁工程技术大学理学院, 阜新 123000;
2. 福建师范大学数学与统计学院, 福州 350117;
3. 北京航空航天大学数学科学学院, 信息与行为教育部重点实验室, 北京 100191
• 收稿日期:2022-07-28 出版日期:2023-05-14 发布日期:2023-05-13
• 通讯作者: 陈彩荣, Email:cairongchen@fjnu.edu.cn
• 基金资助:
国家自然科学基金 (12201275, 11901024, 12131004), 国家重点研发计划 (2021YFA1003600), 辽宁省教育厅基金 (LJ2019JL017, LJ2019JL005) 和福建省自然科学基金 (2021J01661) 资助.

Yu Dongmei, Wang Zengwei, Chen Cairong, Han Deren. A NON-MONOTONE SMOOTHING NEWTON ALGORITHM FOR ABSOLUTE VALUE EQUATIONS ASSOCIATED WITH SECOND-ORDER CONE[J]. Mathematica Numerica Sinica, 2023, 45(2): 251-266.

### A NON-MONOTONE SMOOTHING NEWTON ALGORITHM FOR ABSOLUTE VALUE EQUATIONS ASSOCIATED WITH SECOND-ORDER CONE

Yu Dongmei1, Wang Zengwei1, Chen Cairong2, Han Deren3

1. 1. College of Science, Liaoning Technical University, Fuxin 123000, China;
2. School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, China;
3. School of Mathematical Sciences, Beihang University, LMIB of the Ministry of Education, Beijing 100191, China
• Received:2022-07-28 Online:2023-05-14 Published:2023-05-13

A non-monotone smoothing Newton method is proposed to solve the system of absolute value equations associated with second-order cone. Under certain conditions, we prove that the proposed method is globally and locally quadratically convergent. Numerical results verify that the proposed method can efficiently solve the system of absolute value equations associated with second-order cone.

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