Реферат: 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.

Библиографическая ссылка: Shmyrev V.I.
Polyhedral Complementarity on a Simplex: Search for Fixed Points of Decreasing Regular Mappings
Journal of Applied and Industrial Mathematics. 2019. V.13. N1. P.145-156. DOI: 10.1134/S1990478919010150 Scopus OpenAlex

Оригинальная: Шмырев В.И.
Полиэдральная комплементарность на симплексе: отыскание неподвижных точек убывающих регулярных отображений
Дискретный анализ и исследование операций. 2019. Т.26. №1. С.114-134. РИНЦ

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Scopus:	2-s2.0-85064938518
OpenAlex:	W2942078567

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