Polyhedral complementarity problem with quasimonotone decreasing mappings
The fixed point problem of piecewise constant mappings in Rn is investigated. This is a polyhedral complementarity problem, which is a generalization of the linear complementarity problem. Such mappings arose in the author’s research on the problem of economic equilibrium in exchange models, where m...
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| Format: | Article |
| Language: | English |
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University of Belgrade
2023-01-01
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| Series: | Yugoslav Journal of Operations Research |
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| Online Access: | https://doiserbia.nb.rs/img/doi/0354-0243/2023/0354-02432200031S.pdf |
| _version_ | 1797807519210405888 |
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| author | Shmyrev Vadim I. |
| author_facet | Shmyrev Vadim I. |
| author_sort | Shmyrev Vadim I. |
| collection | DOAJ |
| description | The fixed point problem of piecewise constant mappings in Rn is investigated. This is a polyhedral complementarity problem, which is a generalization of the linear complementarity problem. Such mappings arose in the author’s research on the problem of economic equilibrium in exchange models, where mappings were considered on the price simplex. The author proposed an original approach of polyhedral complementarity, which made it possible to obtain simple algorithms for solving the problem. The present study is a generalization of linear complementarity methods to related problems of a more general nature and reveals a close relationship between linear complementarity and polyhedral complementarity. The investigated method is an analogue of the well-known Lemke method for linear complementarity problems. A class of mappings is described for which the process is monotone, as it is for the linear complementarity problems with positive principal minors of the constraint matrix (class P). It is shown that such a mapping has always unique fixed point. |
| first_indexed | 2024-03-13T06:23:46Z |
| format | Article |
| id | doaj.art-6c8e22ef06d04c56b7ada206ffa7d361 |
| institution | Directory Open Access Journal |
| issn | 0354-0243 1820-743X |
| language | English |
| last_indexed | 2024-03-13T06:23:46Z |
| publishDate | 2023-01-01 |
| publisher | University of Belgrade |
| record_format | Article |
| series | Yugoslav Journal of Operations Research |
| spelling | doaj.art-6c8e22ef06d04c56b7ada206ffa7d3612023-06-09T10:45:23ZengUniversity of BelgradeYugoslav Journal of Operations Research0354-02431820-743X2023-01-0133223924810.2298/YJOR2111016031S0354-02432200031SPolyhedral complementarity problem with quasimonotone decreasing mappingsShmyrev Vadim I.0Sobolev Institute of Mathematics, Novosibirsk, Russia + Novosibirsk State University, Novosibirsk, RussiaThe fixed point problem of piecewise constant mappings in Rn is investigated. This is a polyhedral complementarity problem, which is a generalization of the linear complementarity problem. Such mappings arose in the author’s research on the problem of economic equilibrium in exchange models, where mappings were considered on the price simplex. The author proposed an original approach of polyhedral complementarity, which made it possible to obtain simple algorithms for solving the problem. The present study is a generalization of linear complementarity methods to related problems of a more general nature and reveals a close relationship between linear complementarity and polyhedral complementarity. The investigated method is an analogue of the well-known Lemke method for linear complementarity problems. A class of mappings is described for which the process is monotone, as it is for the linear complementarity problems with positive principal minors of the constraint matrix (class P). It is shown that such a mapping has always unique fixed point.https://doiserbia.nb.rs/img/doi/0354-0243/2023/0354-02432200031S.pdfpolyhedral complementaritypiecewise constant mappingsfixed pointdualitymonotonicityalgorithm |
| spellingShingle | Shmyrev Vadim I. Polyhedral complementarity problem with quasimonotone decreasing mappings Yugoslav Journal of Operations Research polyhedral complementarity piecewise constant mappings fixed point duality monotonicity algorithm |
| title | Polyhedral complementarity problem with quasimonotone decreasing mappings |
| title_full | Polyhedral complementarity problem with quasimonotone decreasing mappings |
| title_fullStr | Polyhedral complementarity problem with quasimonotone decreasing mappings |
| title_full_unstemmed | Polyhedral complementarity problem with quasimonotone decreasing mappings |
| title_short | Polyhedral complementarity problem with quasimonotone decreasing mappings |
| title_sort | polyhedral complementarity problem with quasimonotone decreasing mappings |
| topic | polyhedral complementarity piecewise constant mappings fixed point duality monotonicity algorithm |
| url | https://doiserbia.nb.rs/img/doi/0354-0243/2023/0354-02432200031S.pdf |
| work_keys_str_mv | AT shmyrevvadimi polyhedralcomplementarityproblemwithquasimonotonedecreasingmappings |