TY - JOUR

T1 - Polyhedral complementarity problem with quasimonotone decreasing mappings

AU - Shmyrev, Vadim I.

N1 - The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. 0324-2019-0018). The work was supported in part by the Russian Foundation for Basic Research, project 19-010-0091.

PY - 2023

Y1 - 2023

N2 - The fixed point problem of piecewise constant mappings in Rn is investigated. This is a polyhedral complementarity problem, which is a generalization of the linear complementarity problem. Such mappings arose in the author's research on the problem of economic equilibrium in exchange models, where mappings were considered on the price simplex. The author proposed an original approach of polyhedral complementarity, which made it possible to obtain simple algorithms for solving the problem. The present study is a generalization of linear complementarity methods to related problems of a more general nature and reveals a close relationship between linear complementarity and polyhedral complementarity. The investigated method is an analogue of the well-known Lemke method for linear complementarity problems. A class of mappings is described for which the process is monotone, as it is for the linear complementarity problems with positive principal minors of the constraint matrix (class P). It is shown that such a mapping has always unique fixed point.

AB - The fixed point problem of piecewise constant mappings in Rn is investigated. This is a polyhedral complementarity problem, which is a generalization of the linear complementarity problem. Such mappings arose in the author's research on the problem of economic equilibrium in exchange models, where mappings were considered on the price simplex. The author proposed an original approach of polyhedral complementarity, which made it possible to obtain simple algorithms for solving the problem. The present study is a generalization of linear complementarity methods to related problems of a more general nature and reveals a close relationship between linear complementarity and polyhedral complementarity. The investigated method is an analogue of the well-known Lemke method for linear complementarity problems. A class of mappings is described for which the process is monotone, as it is for the linear complementarity problems with positive principal minors of the constraint matrix (class P). It is shown that such a mapping has always unique fixed point.

KW - Polyhedral complementarity

KW - algorithm

KW - duality

KW - fixed point

KW - monotonicity

KW - piecewise constant mappings

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85161344078&origin=inward&txGid=5d0bdb574f8b9fc33ddaba5721b950f4

UR - https://www.mendeley.com/catalogue/19cd973e-9394-3790-a260-dd934311dcc8/

U2 - 10.2298/YJOR2111016031S

DO - 10.2298/YJOR2111016031S

M3 - Article

VL - 33

SP - 239

EP - 248

JO - Yugoslav Journal of Operations Research

JF - Yugoslav Journal of Operations Research

SN - 0354-0243

IS - 2

ER -