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Diskretn. Anal. Issled. Oper., 2019, Volume 26, Number 1, Pages 114–134 (Mi da920)  

This article is cited in 1 scientific paper (total in 1 paper)

Polyhedral complementarity on a simplex: search for fixed points of decreasing regular mappings

V. I. Shmyrevab

a Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogov Street, 630090 Novosibirsk, Russia

Abstract: We study the problem of finding a fixed point for a special class of piecewise-constant mappings of a simplex into itself which arise in connection with the search for equilibrium prices in the classical exchange model and its various versions. The consideration is based on the polyhedral complementarity which is a natural generalization of linear complementarity. Here we study the mappings arising from models with fixed budgets. Mappings of this class possess a special property of monotonicity (logarithmic monotonicity), which makes it possible to prove that they are potential. We show that the problem of finding fixed points of these mappings is reducible to optimization problems for which it is possible to propose finite suboptimization algorithms. We give description of two algorithms. Illustr. 3, bibliogr. 20.

Keywords: polyhedral complex, complementarity, monotonicity, potentiality, fixed point, suboptimization, algorithm.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00108_а
Russian Academy of Sciences - Federal Agency for Scientific Organizations 227
Siberian Branch of Russian Academy of Sciences


DOI: https://doi.org/10.33048/daio.2019.26.598

Full text: PDF file (381 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2019, 13:1, 145–156

UDC: 519.865.3
Received: 19.10.2017
Revised: 19.09.2018
Accepted:26.09.2018

Citation: V. I. Shmyrev, “Polyhedral complementarity on a simplex: search for fixed points of decreasing regular mappings”, Diskretn. Anal. Issled. Oper., 26:1 (2019), 114–134; J. Appl. Industr. Math., 13:1 (2019), 145–156

Citation in format AMSBIB
\Bibitem{Shm19}
\by V.~I.~Shmyrev
\paper Polyhedral complementarity on a simplex: search for fixed points of~decreasing regular~mappings
\jour Diskretn. Anal. Issled. Oper.
\yr 2019
\vol 26
\issue 1
\pages 114--134
\mathnet{http://mi.mathnet.ru/da920}
\crossref{https://doi.org/10.33048/daio.2019.26.598}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 1
\pages 145--156
\crossref{https://doi.org/10.1134/S1990478919010150}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85064938518}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
  • Дискретный анализ и исследование операций
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