# An approximate lower order penalty approach for solving second-order cone linear complementarity problems

Zijun Hao, Chieu Thanh Nguyen, Jein Shan Chen*

*此作品的通信作者

## 摘要

Based on a class of smoothing approximations to projection function onto second-order cone, an approximate lower order penalty approach for solving second-order cone linear complementarity problems (SOCLCPs) is proposed, and four kinds of specific smoothing approximations are considered. In light of this approach, the SOCLCP is approximated by asymptotic lower order penalty equations with penalty parameter and smoothing parameter. When the penalty parameter tends to positive infinity and the smoothing parameter monotonically decreases to zero, we show that the solution sequence of the asymptotic lower order penalty equations converges to the solution of the SOCLCP at an exponential rate under a mild assumption. A corresponding algorithm is constructed and numerical results are reported to illustrate the feasibility of this approach. The performance profile of four specific smoothing approximations is presented, and the generalization of two approximations are also investigated.

原文 英語 Journal of Global Optimization https://doi.org/10.1007/s10898-021-01116-w 接受/付印 - 2021

• 電腦科學應用
• 控制和優化
• 管理科學與經營研究
• 應用數學