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

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...

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Bibliographic Details
Published in:Applied numerical mathematics 2019-01, Vol.135, p.206-227
Main Authors: Nguyen, Chieu Thanh, Saheya, B., Chang, Yu-Lin, Chen, Jein-Shan
Format: Article
Language:English
Subjects:
Absolute value equations
Second-order cone
Smoothing Newton algorithm
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Summary: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.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2018.08.019