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Mathematical Problems in Engineering
Volume 2017, Article ID 7175385, 8 pages
Research Article

Uniqueness of the Minimal -Norm Solution to the Monotone Linear Complementarity Problem

1Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China
2Department of Public Basic, Wuhan Technology and Business University, Wuhan 430065, China

Correspondence should be addressed to Xiaoqin Jiang; moc.anis@xx_qxgnaij

Received 12 October 2016; Accepted 13 December 2016; Published 4 January 2017

Academic Editor: Wanquan Liu

Copyright © 2017 Ting Zhang and Xiaoqin Jiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The linear complementarity problem (LCP) has wide applications in economic equilibrium, operations research, and so on, which attracted a lot of interest of experts. Finding the sparsest solution to the LCP has real applications in the field of portfolio selection and bimatrix game. Motivated by the approach developed in compressive sensing, we may try to solve an -minimization problem to obtain the sparsest solution to the LCP, where an important theoretical problem is to investigate uniqueness of the solution to the concerned -minimization problem. In this paper, we investigate the problem of finding the minimal -norm solution to the monotone LCP and propose a sufficient and necessary condition for the uniqueness of the minimal -norm solution to the monotone LCP, which provides an important theoretical basis for finding the sparsest solution to the monotone LCP via solving the corresponding -minimization problem. Furthermore, several examples are given to confirm our theoretical finding.