This article is cited in 1 paper

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

V. I. Shmyrev<sup>ab

a</sup> 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.

UDC: 519.865.3

Received: 19.10.2017
Revised: 19.09.2018
Accepted: 26.09.2018

DOI: 10.33048/daio.2019.26.598

 English version: Journal of Applied and Industrial Mathematics, 2019, 13:1, 145–156

Bibliographic databases:

•