| Issue |
RAIRO-Oper. Res.
Volume 54, Number 2, March-April 2020
|
|
|---|---|---|
| Page(s) | 341 - 349 | |
| DOI | https://doi.org/10.1051/ro/2019002 | |
| Published online | 27 February 2020 | |
On the preconditioned projective iterative methods for the linear complementarity problems*
Department of Research Center, Ayandegan Institute of Higher Education, Tonekabon, Mazandaran, Iran
** Corresponding author: saedalatpanah@gmail.com; saedalatpanah@aihe.ac.ir
Received:
5
July
2018
Accepted:
31
December
2018
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.
Mathematics Subject Classification: 90C33 / 65F10
Key words: Linear complementarity problems / preconditioning / Projected model / M-matrix / GAOR
© EDP Sciences, ROADEF, SMAI 2020
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