### Abstract

In this paper, we explore a unified way to construct smoothing functions for solving the absolute value equation associated with second-order cone (SOCAVE). Numerical comparisons are presented, which illustrate what kinds of smoothing functions work well along with the smoothing Newton algorithm. In particular, the numerical experiments show that the well known loss function widely used in engineering community is the worst one among the constructed smoothing functions, which indicates that the other proposed smoothing functions can be employed for solving engineering problems.

Original language | English |
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Pages (from-to) | 206-227 |

Number of pages | 22 |

Journal | Applied Numerical Mathematics |

Volume | 135 |

DOIs | |

Publication status | Published - 2019 Jan 1 |

### Keywords

- Absolute value equations
- Second-order cone
- Smoothing Newton algorithm

### ASJC Scopus subject areas

- Numerical Analysis
- Computational Mathematics
- Applied Mathematics

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## Cite this

Nguyen, C. T., Saheya, B., Chang, Y. L., & Chen, J. S. (2019). Unified smoothing functions for absolute value equation associated with second-order cone.

*Applied Numerical Mathematics*,*135*, 206-227. https://doi.org/10.1016/j.apnum.2018.08.019