# American Institute of Mathematical Sciences

January  2010, 6(1): 259-267. doi: 10.3934/jimo.2010.6.259

## A potential reduction method for the generalized linear complementarity problem over a polyhedral cone

 1 School of Operations Research and Management Science, Qufu Normal University, Rizhao Shandong, 276800, China 2 School of Management Science, Qufu Normal University, Rizhao Shandong, 276800 3 The Fundamental Department of Mathematics, Shandong Water Polytechnic College, Rizhao Shandong, 276800, China

Received  March 2009 Revised  October 2009 Published  November 2009

In this paper, we consider the generalized linear complementarity problem over a polyhedral cone arising in economics and engineering. For this problem, we first discuss its solution existence and then propose a potential reduction algorithm to solve it. The sparseness of the involved coefficient matrix is fully exploited in the computation of the algorithm and hence it has a relatively lower computational cost. The global convergence of the method is obtained under milder conditions. The given preliminary numerical experiments show the efficiency of the method.
Citation: Fengming Ma, Yiju Wang, Hongge Zhao. A potential reduction method for the generalized linear complementarity problem over a polyhedral cone. Journal of Industrial & Management Optimization, 2010, 6 (1) : 259-267. doi: 10.3934/jimo.2010.6.259
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