Polyhedral complementarity on a simplex. Method of meeting paths for decreasing quasi-regular mappings. [ПОЛИЭДРАЛЬНАЯ КОМПЛЕМЕНТАРНОСТЬ НА СИМПЛЕКСЕ. МЕТОД ВСТРЕЧНЫХ ПУТЕЙ ДЛЯ УБЫВАЮЩИХ КВАЗИРЕГУЛЯРНЫХ ОТОБРАЖЕНИЙ1] Full article
| Journal |
Труды Института математики и механики УрО РАН (Trudy Instituta Matematiki i Mekhaniki UrO RAN)
ISSN: 0134-4889 , E-ISSN: 2658-4786 |
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| Output data | Year: 2019, Volume: 25, Number: 2, Pages: 273-286 Pages count : 14 DOI: 10.21538/0134-4889-2019-25-2-273-286 | ||||
| Tags | Algorithm; Complementarity; Fixed point; Monotonicity; Polyhedral complex; Simplex | ||||
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Abstract:
The paper explores the mathematical basis of a novel polyhedral complementarity approach proposed by the author for finding an economic equilibrium in a linear exchange model and its variations. The equilibrium problem reduces to finding fixed points of point-to-set mappings of the price simplex to itself. As a result, we obtain a polyhedral complementarity problem generated by a pair of polyhedral complexes in duality. The class of quasi-regular mappings, which is a new class of decreasing mappings having no analogs in Rn, is considered. The procedure of meeting paths, which generalizes the known Lemke method for linear complementarity problems, is studied. It is shown that in the case under consideration the procedure has the property of monotonicity characteristic of linear complementarity problems with positive principal minors of the constraint matrix (P-class). The uniqueness of the desired fixed point is a consequence of monotonicity. © 2019 Krasovskii Institute of Mathematics and Mechanics. All right reserved.
Cite:
Shmyrev V.I.
Polyhedral complementarity on a simplex. Method of meeting paths for decreasing quasi-regular mappings. [ПОЛИЭДРАЛЬНАЯ КОМПЛЕМЕНТАРНОСТЬ НА СИМПЛЕКСЕ. МЕТОД ВСТРЕЧНЫХ ПУТЕЙ ДЛЯ УБЫВАЮЩИХ КВАЗИРЕГУЛЯРНЫХ ОТОБРАЖЕНИЙ1]
Труды Института математики и механики УрО РАН (Trudy Instituta Matematiki i Mekhaniki UrO RAN). 2019. Т.25. №2. С.273-286. DOI: 10.21538/0134-4889-2019-25-2-273-286 WOS Scopus OpenAlex
Polyhedral complementarity on a simplex. Method of meeting paths for decreasing quasi-regular mappings. [ПОЛИЭДРАЛЬНАЯ КОМПЛЕМЕНТАРНОСТЬ НА СИМПЛЕКСЕ. МЕТОД ВСТРЕЧНЫХ ПУТЕЙ ДЛЯ УБЫВАЮЩИХ КВАЗИРЕГУЛЯРНЫХ ОТОБРАЖЕНИЙ1]
Труды Института математики и механики УрО РАН (Trudy Instituta Matematiki i Mekhaniki UrO RAN). 2019. Т.25. №2. С.273-286. DOI: 10.21538/0134-4889-2019-25-2-273-286 WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000485177500023 |
| Scopus: | 2-s2.0-85078230720 |
| OpenAlex: | W4237474005 |