Targeting modulus-based matrix splitting iteration approach for the second-order cone linear complementarity model of three-dimensional frictional contact problems.
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| Title: | Targeting modulus-based matrix splitting iteration approach for the second-order cone linear complementarity model of three-dimensional frictional contact problems. |
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| Authors: | Li, Zhizhi1 (AUTHOR) lizhizhi16@mails.ucas.ac.cn, Jin, Yimin2 (AUTHOR) jinyimin14@mails.ucas.ac.cn, Zhang, Huai1 (AUTHOR) hzhang@ucas.ac.cn |
| Source: | Optimization & Engineering. Jun2026, Vol. 27 Issue 2, p1579-1610. 32p. |
| Subjects: | Computational complexity, Linear complementarity problem, Newton-Raphson method, Iterative methods (Mathematics), Matrix decomposition |
| Abstract: | The second-order cone linear complementarity problem (SOCLCP) can be used as a model of contact problems with friction. However, its standard formulation as a SOCLCP cannot be employed to large 3d problems because it requires a matrix inversion, which has a computational complexity of O (N uo 3) . Therefore and here, inspired by the flexibility and structural simplicity of the well known MMS algorithms, we propose the Targeting-MMS algorithm for the SOCLCP model of 3d contact problems with friction. The computational complexity is reduced to O (N uo 2) (or even to O (N uo) ). More importantly, we theoretically provide the optimal parameter for the new algorithm, which is a key point for a iteration method. Numerical results show that the Targeting-MMS algorithm with the proposed optimal parameter can save 85 % - 90 % of the time overhead compared to the MMS algorithms and the semi-smooth Newton method, which are by far the state-of-the-art and commonly used methods for solving the SOCLCP. [ABSTRACT FROM AUTHOR] |
| Copyright of Optimization & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Targeting modulus-based matrix splitting iteration approach for the second-order cone linear complementarity model of three-dimensional frictional contact problems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Li%2C+Zhizhi%22">Li, Zhizhi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> lizhizhi16@mails.ucas.ac.cn</i><br /><searchLink fieldCode="AR" term="%22Jin%2C+Yimin%22">Jin, Yimin</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> jinyimin14@mails.ucas.ac.cn</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Huai%22">Zhang, Huai</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hzhang@ucas.ac.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Optimization+%26+Engineering%22">Optimization & Engineering</searchLink>. Jun2026, Vol. 27 Issue 2, p1579-1610. 32p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+complementarity+problem%22">Linear complementarity problem</searchLink><br /><searchLink fieldCode="DE" term="%22Newton-Raphson+method%22">Newton-Raphson method</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+decomposition%22">Matrix decomposition</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The second-order cone linear complementarity problem (SOCLCP) can be used as a model of contact problems with friction. However, its standard formulation as a SOCLCP cannot be employed to large 3d problems because it requires a matrix inversion, which has a computational complexity of O (N uo 3) . Therefore and here, inspired by the flexibility and structural simplicity of the well known MMS algorithms, we propose the Targeting-MMS algorithm for the SOCLCP model of 3d contact problems with friction. The computational complexity is reduced to O (N uo 2) (or even to O (N uo) ). More importantly, we theoretically provide the optimal parameter for the new algorithm, which is a key point for a iteration method. Numerical results show that the Targeting-MMS algorithm with the proposed optimal parameter can save 85 % - 90 % of the time overhead compared to the MMS algorithms and the semi-smooth Newton method, which are by far the state-of-the-art and commonly used methods for solving the SOCLCP. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Optimization & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s11081-025-10066-1 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 32 StartPage: 1579 Subjects: – SubjectFull: Computational complexity Type: general – SubjectFull: Linear complementarity problem Type: general – SubjectFull: Newton-Raphson method Type: general – SubjectFull: Iterative methods (Mathematics) Type: general – SubjectFull: Matrix decomposition Type: general Titles: – TitleFull: Targeting modulus-based matrix splitting iteration approach for the second-order cone linear complementarity model of three-dimensional frictional contact problems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Li, Zhizhi – PersonEntity: Name: NameFull: Jin, Yimin – PersonEntity: Name: NameFull: Zhang, Huai IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13894420 Numbering: – Type: volume Value: 27 – Type: issue Value: 2 Titles: – TitleFull: Optimization & Engineering Type: main |
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