Smoothing penalty approach for solving second-order cone complementarity problems
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...
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| Published in | Journal of global optimization Vol. 91; no. 1; pp. 39 - 58 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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New York
Springer US
01.01.2025
Springer Nature B.V |
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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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| AbstractList | 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. |
| Author | Chen, Jein-Shan Hao, Zijun Nguyen, Chieu Thanh Alcantara, Jan Harold |
| Author_xml | – sequence: 1 givenname: Chieu Thanh surname: Nguyen fullname: Nguyen, Chieu Thanh organization: Department of Mathematics, Faculty of Information Technology, Vietnam National University of Agriculture – sequence: 2 givenname: Jan Harold surname: Alcantara fullname: Alcantara, Jan Harold organization: Center for Advanced Intelligence Project, RIKEN – sequence: 3 givenname: Zijun surname: Hao fullname: Hao, Zijun organization: School of Mathematics and Information Science, North Minzu University – sequence: 4 givenname: Jein-Shan orcidid: 0000-0002-4596-9419 surname: Chen fullname: Chen, Jein-Shan email: jschen@math.ntnu.edu.tw organization: Department of Mathematics, National Taiwan Normal University |
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| References | L Chen (1427_CR12) 2011; 61 J-S Chen (1427_CR11) 2005; 104 J Sun (1427_CR33) 2021; 32 B Tian (1427_CR34) 2015; 62 S Hayashi (1427_CR23) 2005; 15 M Fukushima (1427_CR18) 2002; 12 MC Ferris (1427_CR17) 1997; 39 A Auslender (1427_CR4) 2003; 18 L-H Zhang (1427_CR37) 2014; 24 B Tian (1427_CR35) 2016; 12 F Alizadeh (1427_CR3) 2003; 95 S Hayashi (1427_CR24) 2005; 6 L Qi (1427_CR32) 2011; 32 J Chen (1427_CR8) 2008; 213 MS Lobo (1427_CR28) 1998; 284 J-S Chen (1427_CR9) 2019 R Monteiro (1427_CR30) 2000; 88 JH Alcantara (1427_CR2) 2024 SC Billups (1427_CR5) 2000; 124 C Chen (1427_CR6) 1996; 5 J Chen (1427_CR7) 2006; 64 X Chen (1427_CR13) 2003; 25 J Faraut (1427_CR16) 1994 Z Hao (1427_CR20) 2015; 290 J-S Chen (1427_CR10) 2004; 101 C Kanzow (1427_CR27) 2009; 20 Z-H Huang (1427_CR26) 2010; 45 S Pan (1427_CR31) 2009; 70 S Wang (1427_CR36) 2008; 36 S Hayashi (1427_CR22) 2005; 15 X Miao (1427_CR29) 2014; 268 L Cheng (1427_CR14) 2020; 75 C Huang (1427_CR25) 2010; 38 JH Alcantara (1427_CR1) 2022; 407 S Hayashi (1427_CR21) 2005; 175 F Facchinei (1427_CR15) 2003 Z Hao (1427_CR19) 2022; 83 |
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| SubjectTerms | Algorithms Approximation Computer Science Mathematics Mathematics and Statistics Methods Nonlinear equations Operations Research/Decision Theory Optimization Real Functions Smoothing Tensors |
| Title | Smoothing penalty approach for solving second-order cone complementarity problems |
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