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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Bibliographic Details
Published inOptimization Vol. 56; no. 3; pp. 399 - 416
Main Author Konnov, I. V.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis Group 01.06.2007
Taylor & Francis LLC
Subjects
Algorithms
Existence of solutions
Jacobi algorithm
Linear algebra
Mapping
Mathematics Subject Classification 2000
Mixed complementarity problem
Multi-valued mappings
Studies
Upper Z-mappings
Online AccessGet full text
ISSN0233-1934
1029-4945
DOI10.1080/02331930600662856

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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331930600662856