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Unified smoothing functions for absolute value equation associated with second-order cone

Chieu Thanh Nguyen B Saheya Yu-Lin Chang Jein-Shan Chen

Numerical Analysis and Scientific Computing mathscidoc:1910.43946

Applied Numerical Mathematics, 135, 206-227, 2019.1
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.
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@inproceedings{chieu2019unified,
  title={Unified smoothing functions for absolute value equation associated with second-order cone},
  author={Chieu Thanh Nguyen, B Saheya, Yu-Lin Chang, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020225749627124475},
  booktitle={Applied Numerical Mathematics},
  volume={135},
  pages={206-227},
  year={2019},
}
Chieu Thanh Nguyen, B Saheya, Yu-Lin Chang, and Jein-Shan Chen. Unified smoothing functions for absolute value equation associated with second-order cone. 2019. Vol. 135. In Applied Numerical Mathematics. pp.206-227. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020225749627124475.
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