An extension of the Jacobi algorithm for multi-valued mixed complementarity problems
We consider a generalized mixed complementarity problem (MCP) with box constraints and multi-valued cost mapping. We introduce a concept of an upper Z-mapping, which generalizes the well-known concept of the single-valued Z-mapping and involves the diagonal multi-valued mappings, and suggest an exte...
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| Published in | Optimization Vol. 56; no. 3; pp. 399 - 416 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Taylor & Francis Group
01.06.2007
Taylor & Francis LLC |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0233-1934 1029-4945 |
| DOI | 10.1080/02331930600662856 |
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| Abstract | We consider a generalized mixed complementarity problem (MCP) with box constraints and multi-valued cost mapping. We introduce a concept of an upper Z-mapping, which generalizes the well-known concept of the single-valued Z-mapping and involves the diagonal multi-valued mappings, and suggest an extension of the Jacobi algorithm for the above problem containing a composition of such mappings. Being based on its convergence theorem, we establish several existence and uniqueness results. Some examples of the applications are also given. |
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| AbstractList | We consider a generalized mixed complementarity problem (MCP) with box constraints and multi-valued cost mapping. We introduce a concept of an upper Z-mapping, which generalizes the well-known concept of the single-valued Z-mapping and involves the diagonal multi-valued mappings, and suggest an extension of the Jacobi algorithm for the above problem containing a composition of such mappings. Being based on its convergence theorem, we establish several existence and uniqueness results. Some examples of the applications are also given. [PUBLICATION ABSTRACT] We consider a generalized mixed complementarity problem (MCP) with box constraints and multi-valued cost mapping. We introduce a concept of an upper Z-mapping, which generalizes the well-known concept of the single-valued Z-mapping and involves the diagonal multi-valued mappings, and suggest an extension of the Jacobi algorithm for the above problem containing a composition of such mappings. Being based on its convergence theorem, we establish several existence and uniqueness results. Some examples of the applications are also given. |
| Author | Konnov, I. V. |
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| Cites_doi | 10.1007/978-3-662-02622-9 10.2478/cmam-2002-0002 10.1007/BF01580248 10.1155/S1110757X02106012 10.1137/S0036144595285963 10.1007/BFb0084653 10.1287/moor.6.3.462 10.1016/0022-247X(70)90298-2 10.1137/0318005 10.1007/978-3-642-56886-2 10.1007/BF01585501 10.1016/0024-3795(73)90006-2 10.1023/A:1021724306242 |
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| References | Nikaido H (CIT0006) 1968 Baiocchi C (CIT0011) 1984 Lapin AV (CIT0016) 2001 Isac G (CIT0002) 1992 Okuguchi K (CIT0021) 1990 Konnov IV (CIT0012) 2001 Lapin AV (CIT0017) 2002; 2 Cottle RW (CIT0001) 1992 Malishevskii AV (CIT0018) 1969; 30 Polterovich VM (CIT0010) 1982; 19 Konnov IV (CIT0020) 2003; 6 CIT0003 CIT0014 CIT0013 CIT0005 CIT0004 CIT0007 CIT0009 Malishevskii AV (CIT0015) 1972; 33 CIT0008 CIT0019 |
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| SubjectTerms | Algorithms Existence of solutions Jacobi algorithm Linear algebra Mapping Mathematics Subject Classification 2000 Mixed complementarity problem Multi-valued mappings Studies Upper Z-mappings |
| Title | An extension of the Jacobi algorithm for multi-valued mixed complementarity problems |
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