Smoothing penalty approach for solving second-order cone complementarity problems

Chieu Thanh Nguyen; Jan Harold Alcantara; Zijun Hao; Jein Shan Chen

doi:10.1007/s10898-024-01427-8

Smoothing penalty approach for solving second-order cone complementarity problems

Chieu Thanh Nguyen, Jan Harold Alcantara, Zijun Hao, Jein Shan Chen^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we propose a smoothing penalty approach for solving the second-order cone complementarity problem (SOCCP). The SOCCP is approximated by a smooth nonlinear equation with penalization parameter. We show that any solution sequence of the approximating equations converges to the solution of the SOCCP under the assumption that the associated function of the SOCCP satisfies a uniform Cartesian-type property. We present a corresponding algorithm for solving the SOCCP based on this smoothing penalty approach, and we demonstrate the efficiency of our method for solving linear, nonlinear and tensor complementarity problems in the second-order cone setting.

Original language	English
Article number	114092
Pages (from-to)	39-58
Number of pages	20
Journal	Journal of Global Optimization
Volume	91
Issue number	1
DOIs	https://doi.org/10.1007/s10898-024-01427-8
Publication status	Published - 2025 Jan

Keywords

Nonlinear complementarity problem
Penalty method
Second-order cone

ASJC Scopus subject areas

Business, Management and Accounting (miscellaneous)
Computer Science Applications
Control and Optimization
Management Science and Operations Research
Applied Mathematics

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10.1007/s10898-024-01427-8

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abstract = "In this paper, we propose a smoothing penalty approach for solving the second-order cone complementarity problem (SOCCP). The SOCCP is approximated by a smooth nonlinear equation with penalization parameter. We show that any solution sequence of the approximating equations converges to the solution of the SOCCP under the assumption that the associated function of the SOCCP satisfies a uniform Cartesian-type property. We present a corresponding algorithm for solving the SOCCP based on this smoothing penalty approach, and we demonstrate the efficiency of our method for solving linear, nonlinear and tensor complementarity problems in the second-order cone setting.",

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AU - Alcantara, Jan Harold

AU - Hao, Zijun

AU - Chen, Jein Shan

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

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AB - In this paper, we propose a smoothing penalty approach for solving the second-order cone complementarity problem (SOCCP). The SOCCP is approximated by a smooth nonlinear equation with penalization parameter. We show that any solution sequence of the approximating equations converges to the solution of the SOCCP under the assumption that the associated function of the SOCCP satisfies a uniform Cartesian-type property. We present a corresponding algorithm for solving the SOCCP based on this smoothing penalty approach, and we demonstrate the efficiency of our method for solving linear, nonlinear and tensor complementarity problems in the second-order cone setting.

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KW - Penalty method

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Smoothing penalty approach for solving second-order cone complementarity problems

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Keywords

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