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Sib. Zh. Ind. Mat., 2018, Volume 21, Number 1, Pages 118–128 (Mi sjim994)  

This article is cited in 2 scientific papers (total in 2 papers)

Polyhedral complementarity on a simplex. Potentiality of regular mappings

V. I. Shmyrevab

a Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
b Novosibirsk State University, 2 Pirogova str., 630090 Novosibirsk

Abstract: We consider a special class of the fixed point problems for piecewise constant mappings of a simplex into itself. These are polyhedral complementarity problems arising in studying the classical exchange model and its variations. We study the problems that stem from the consideration of models with fixed budgets and possessing a certain property of monotonicity (logarithmic monotonicity). Our considerations are purely mathematical and not associated with the economic models that gave rise to these mathematical objects. The class of regular mappings is investigated, and their potentiality is proved.

Keywords: linear complementarity, polyhedral complex, monotonicity, potentiality of mapping, homology group.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00108-а


DOI: https://doi.org/10.17377/sibjim.2018.21.000

Full text: PDF file (291 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2018, 12:1, 167–176

UDC: 519.865.3
Received: 02.03.2017

Citation: V. I. Shmyrev, “Polyhedral complementarity on a simplex. Potentiality of regular mappings”, Sib. Zh. Ind. Mat., 21:1 (2018), 118–128; J. Appl. Industr. Math., 12:1 (2018), 167–176

Citation in format AMSBIB
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\by V.~I.~Shmyrev
\paper Polyhedral complementarity on a~simplex. Potentiality of regular mappings
\jour Sib. Zh. Ind. Mat.
\yr 2018
\vol 21
\issue 1
\pages 118--128
\mathnet{http://mi.mathnet.ru/sjim994}
\crossref{https://doi.org/10.17377/sibjim.2018.21.000}
\elib{http://elibrary.ru/item.asp?id=32872887}
\transl
\jour J. Appl. Industr. Math.
\yr 2018
\vol 12
\issue 1
\pages 167--176
\crossref{https://doi.org/10.1134/S1990478918010155}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85043239409}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Shmyrev, “Polyhedral complementarity on a simplex: search for fixed points of decreasing regular mappings”, J. Appl. Industr. Math., 13:1 (2019), 145–156  mathnet  crossref  crossref
    2. V. I. Shmyrev, “Poliedralnaya komplementarnost na simplekse. metod vstrechnykh putei dlya ubyvayuschikh kvaziregulyarnykh otobrazhenii”, Tr. IMM UrO RAN, 25, no. 2, 2019, 273–286  mathnet  crossref  elib
  • Сибирский журнал индустриальной математики
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