Abstract: 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.

Cite: Shmyrev V.I.
Polyhedral Complementarity Problem With Quasimonotone Decreasing Mappings
Yugoslav Journal of Operations Research. 2023. V.33. N2. P.239-248. DOI: 10.2298/YJOR2111016031S Scopus РИНЦ OpenAlex

Dates:

Submitted:	Nov 10, 2021
Accepted:	Nov 10, 2022
Published online:	Dec 15, 2022
Published print:	Jan 20, 2023

Identifiers:

Scopus:	2-s2.0-85161344078
Elibrary:	60239000
OpenAlex:	W4312668273

Citing: Пока нет цитирований

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