TY - JOUR

T1 - Polyhedral Complementarity on a Simplex

T2 - Search for Fixed Points of Decreasing Regular Mappings

AU - Shmyrev, V. I.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - algorithm

KW - complementarity

KW - fixed point

KW - monotonicity

KW - polyhedral complex

KW - potentiality

KW - suboptimization

UR - http://www.scopus.com/inward/record.url?scp=85064938518&partnerID=8YFLogxK

U2 - 10.1134/S1990478919010150

DO - 10.1134/S1990478919010150

M3 - Article

AN - SCOPUS:85064938518

VL - 13

SP - 145

EP - 156

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

ER -