Research output: Contribution to journal › Article › peer-review
Polyhedral complementarity problem with quasimonotone decreasing mappings. / Shmyrev, Vadim I.
In: Yugoslav Journal of Operations Research, Vol. 33, No. 2, 2023, p. 239-248.Research output: Contribution to journal › Article › peer-review
}
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 -
ID: 56585334