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

Chieu Thanh Nguyen, B. Saheya, Yu Lin Chang, Jein Shan Chen

Research output: Contribution to journalArticle

1 Citation (Scopus)

### 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 206-227 22 Applied Numerical Mathematics 135 https://doi.org/10.1016/j.apnum.2018.08.019 Published - 2019 Jan 1

### Fingerprint

Smoothing Function
Second-order Cone
Absolute value
Cones
Engineering
Numerical Comparisons
Loss Function
Smoothing
Numerical Experiment
Experiments

### Keywords

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

### ASJC Scopus subject areas

• Numerical Analysis
• Computational Mathematics
• Applied Mathematics

### Cite this

Unified smoothing functions for absolute value equation associated with second-order cone. / Nguyen, Chieu Thanh; Saheya, B.; Chang, Yu Lin; Chen, Jein Shan.

In: Applied Numerical Mathematics, Vol. 135, 01.01.2019, p. 206-227.

Research output: Contribution to journalArticle

@article{0a3d36863eb74028b6df39040f2082dd,
title = "Unified smoothing functions for absolute value equation associated with second-order cone",
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.",
keywords = "Absolute value equations, Second-order cone, Smoothing Newton algorithm",
author = "Nguyen, {Chieu Thanh} and B. Saheya and Chang, {Yu Lin} and Chen, {Jein Shan}",
year = "2019",
month = "1",
day = "1",
doi = "10.1016/j.apnum.2018.08.019",
language = "English",
volume = "135",
pages = "206--227",
journal = "Applied Numerical Mathematics",
issn = "0168-9274",
publisher = "Elsevier",

}

TY - JOUR

T1 - Unified smoothing functions for absolute value equation associated with second-order cone

AU - Nguyen, Chieu Thanh

AU - Saheya, B.

AU - Chang, Yu Lin

AU - Chen, Jein Shan

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Absolute value equations

KW - Second-order cone

KW - Smoothing Newton algorithm

UR - http://www.scopus.com/inward/record.url?scp=85053054309&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053054309&partnerID=8YFLogxK

U2 - 10.1016/j.apnum.2018.08.019

DO - 10.1016/j.apnum.2018.08.019

M3 - Article

AN - SCOPUS:85053054309

VL - 135

SP - 206

EP - 227

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -