Research Article | OPEN ACCESS
A Power Penalty Approach to a Horizontal Linear Complementarity Problem
1Xizhen Hu, 1Chongchao Huang, 1, 2Aihua Luo, 1, 3Hua Chen
1Department of Mathematics and Statistics, Wuhan University, Wuhan, 430012, China
2Department of Mathematics and Statistics, South-Central University for
Nationalities, Wuhan, 430074, China
3Department of science, Hubei University of Technology, Wuhan, 430068, China
Research Journal of Applied Sciences, Engineering and Technology 2013 5:1830-1835
Received: August 11, 2012 | Accepted: September 03, 2012 | Published: February 11, 2013
Abstract
A power penalty approach has been proposed to linear complementarity problem but not to Horizontal Linear Complementarity Problem (HLCP) because the coefficient matrix is not positive definite. It is skillfully proved that HLCP is equivalent to a variational inequality problem and a mixed linear complementarity problem for the first time. A power penalty approach is proposed to the mixed linear complementarity problem based on approximating the HLP by a nonlinear equation. It has been proved that the solution to this equation is feasible and converges to that of the HLP at a rate of at least O(&lambda)-k/2 in the Euclidean norm.
Keywords:
Convergence rate, horizontal linear complementarity problem, power penalty methods, strong monotone, variational inequality,
Competing interests
The authors have no competing interests.
Open Access Policy
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Copyright
The authors have no competing interests.
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ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
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