A modulus-based matrix splitting method for the vertical nonlinear complementarity problem
Many applications arising in control theory, nonlinear networks, generalized Leontief input–output model and economics lead to a broad range of optimization and equilibrium problems. Under suitable convexity assumptions, the equilibrium conditions of such problems may be compactly stated as the vert...
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| Veröffentlicht in: | Journal of applied mathematics & computing 2023-08, Vol.69 (4), p.2987-3003 |
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| container_title | Journal of applied mathematics & computing |
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| creator | Xie, Shuilian Yang, Zhen-Ping Xu, Hongru |
| description | Many applications arising in control theory, nonlinear networks, generalized Leontief input–output model and economics lead to a broad range of optimization and equilibrium problems. Under suitable convexity assumptions, the equilibrium conditions of such problems may be compactly stated as the vertical nonlinear complementarity problem (VNCP). In this paper, based on modulus-based formulation of the VNCP, we present a variety of modulus-based matrix splitting methods for solving the VNCP. Under some mild conditions, we establish the convergence of the proposed method. Numerical experiments indicate that the proposed method is effective. |
| doi_str_mv | 10.1007/s12190-023-01866-8 |
| format | Article |
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Numerical experiments indicate that the proposed method is effective.</description><subject>Applied mathematics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Control theory</subject><subject>Convexity</subject><subject>Economic models</subject><subject>Equilibrium conditions</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics of Computing</subject><subject>Nonlinear control</subject><subject>Optimization</subject><subject>Original Research</subject><subject>Splitting</subject><subject>Theory of Computation</subject><issn>1598-5865</issn><issn>1865-2085</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9UE1PxCAQJUYT19U_4InEMwq0UDhuNuqabOJFL14IULrbTVsqUOP-e9GaePM0b2beR_IAuCb4lmBc3UVCicQI0wJhIjhH4gQsMmCIYsFOM2ZSIJYP5-AixgPGvJJYLsDbCva-nropIqOjq2GvU2g_YRy7NqV22MHepb2vYeMDTHsHP1xIrdUdHPzQtYPTAVrfj53r3ZB0aNMRjsGbvF-Cs0Z30V39ziV4fbh_WW_Q9vnxab3aIlsQmRArSopZw5jRlSwrwo2xlFKjrZFcN7q0QjPuuGU2_6hpSlbUFXFcCiNrZ4oluJl9c-775GJSBz-FIUcqKgopCGMlziw6s2zwMQbXqDG0vQ5HRbD67lDNHarcofrpUIksKmZRzORh58Kf9T-qL-ghdk4</recordid><startdate>20230801</startdate><enddate>20230801</enddate><creator>Xie, Shuilian</creator><creator>Yang, Zhen-Ping</creator><creator>Xu, Hongru</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20230801</creationdate><title>A modulus-based matrix splitting method for the vertical nonlinear complementarity problem</title><author>Xie, Shuilian ; Yang, Zhen-Ping ; Xu, Hongru</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-534205f55ba794716bbc222bacb96afa4c8a56e6c5c16b2bf453d71e698b9deb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Applied mathematics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Control theory</topic><topic>Convexity</topic><topic>Economic models</topic><topic>Equilibrium conditions</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics of Computing</topic><topic>Nonlinear control</topic><topic>Optimization</topic><topic>Original Research</topic><topic>Splitting</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xie, Shuilian</creatorcontrib><creatorcontrib>Yang, Zhen-Ping</creatorcontrib><creatorcontrib>Xu, Hongru</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of applied mathematics & computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Xie, Shuilian</au><au>Yang, Zhen-Ping</au><au>Xu, Hongru</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A modulus-based matrix splitting method for the vertical nonlinear complementarity problem</atitle><jtitle>Journal of applied mathematics & computing</jtitle><stitle>J. 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| subjects | Applied mathematics Computational Mathematics and Numerical Analysis Control theory Convexity Economic models Equilibrium conditions Mathematical and Computational Engineering Mathematics Mathematics and Statistics Mathematics of Computing Nonlinear control Optimization Original Research Splitting Theory of Computation |
| title | A modulus-based matrix splitting method for the vertical nonlinear complementarity problem |
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