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Trudy Inst. Mat. i Mekh. UrO RAN, 2019, Volume 25, Number 2, Pages 273–286 (Mi timm1641)  

Polyhedral complementarity on a simplex. method of meeting paths for decreasing quasi-regular mappings

V. I. Shmyrevab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

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 $\mathbb{R}^n$, 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.

Keywords: simplex, polyhedral complex, complementarity, monotonicity, fixed point, algorithm.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-010-00910 А
Russian Academy of Sciences - Federal Agency for Scientific Organizations 227
Siberian Branch of Russian Academy of Sciences
This work was supported by the Russian Foundation for Basic Research (project no. 19-010-00910 A), by Program no. 227 of the Presidium of the Russian Academy of Sciences, and by Interdisciplinary Integration Project no. 7B of the Siberian Branch of the Russian Academy of Sciences.


DOI: https://doi.org/10.21538/0134-4889-2019-25-2-273-286

Full text: PDF file (257 kB)
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Bibliographic databases:

UDC: 519.865.3
MSC: 90C33, 90-08
Received: 28.01.2019

Citation: V. I. Shmyrev, “Polyhedral complementarity on a simplex. method of meeting paths for decreasing quasi-regular mappings”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 2, 2019, 273–286

Citation in format AMSBIB
\Bibitem{Shm19}
\by V.~I.~Shmyrev
\paper Polyhedral complementarity on a simplex. method of meeting paths for decreasing quasi-regular mappings
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2019
\vol 25
\issue 2
\pages 273--286
\mathnet{http://mi.mathnet.ru/timm1641}
\crossref{https://doi.org/10.21538/0134-4889-2019-25-2-273-286}
\elib{https://elibrary.ru/item.asp?id=38071621}


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