Polyhedral Complementarity on a Simplex: Search for Fixed Points of Decreasing Regular Mappings

被引：0

作者：

Shmyrev V.I. ^{[1
,2
]}

机构：

[1] Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk

[2] Novosibirsk State University, ul. Pirogova 2, Novosibirsk

来源：

Journal of Applied and Industrial Mathematics | 2019年 / 13卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

algorithm; complementarity; fixed point; monotonicity; polyhedral complex; potentiality; suboptimization;

D O I：

10.1134/S1990478919010150

中图分类号：

学科分类号：

摘要：

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. © 2019, Pleiades Publishing, Ltd.

引用

页码：145 / 156

页数：11

共 20 条

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