This paper aims to propose the new preconditioning approaches for solving linear complementarity problem (LCP). Some years ago, the preconditioned projected iterative methods were presented for the solution of the LCP, and the convergence of these methods has been analyzed. However, most of these methods are not correct, and this is because the complementarity condition of the preconditioned LCP is not always equivalent to that of the un-preconditioned original LCP. To overcome this shortcoming, we present a new strategy with a new preconditioner that ensures the solution of the same problem is correct. We also study the convergence properties of the new preconditioned iterative method for solving LCP. Finally, the new approach is illustrated with the help of a numerical example.
Keywords: Linear complementarity problems, preconditioning, Projected model, $$-matrix, GAOR
@article{RO_2020__54_2_341_0,
author = {Edalatpanah, Seyyed Ahmad},
title = {On the preconditioned projective iterative methods for the linear complementarity problems},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {341--349},
year = {2020},
publisher = {EDP Sciences},
volume = {54},
number = {2},
doi = {10.1051/ro/2019002},
mrnumber = {4069302},
zbl = {1443.90317},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2019002/}
}
TY - JOUR AU - Edalatpanah, Seyyed Ahmad TI - On the preconditioned projective iterative methods for the linear complementarity problems JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2020 SP - 341 EP - 349 VL - 54 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ro/2019002/ DO - 10.1051/ro/2019002 LA - en ID - RO_2020__54_2_341_0 ER -
%0 Journal Article %A Edalatpanah, Seyyed Ahmad %T On the preconditioned projective iterative methods for the linear complementarity problems %J RAIRO - Operations Research - Recherche Opérationnelle %D 2020 %P 341-349 %V 54 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ro/2019002/ %R 10.1051/ro/2019002 %G en %F RO_2020__54_2_341_0
Edalatpanah, Seyyed Ahmad. On the preconditioned projective iterative methods for the linear complementarity problems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 2, pp. 341-349. doi: 10.1051/ro/2019002
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