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Journal of Industrial and Management Optimization (JIMO)
 

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

Pages: 259 - 267, Volume 6, Issue 1, February 2010      doi:10.3934/jimo.2010.6.259

 
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Fengming Ma - School of Operations Research and Management Science, Qufu Normal University, Rizhao Shandong, 276800, China (email)
Yiju Wang - School of Management Science, Qufu Normal University, Rizhao Shandong, 276800, China (email)
Hongge Zhao - The Fundamental Department of Mathematics, Shandong Water Polytechnic College, Rizhao Shandong, 276800, China (email)

Abstract: 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.

Keywords:  GLCP, existence of solutions, potential reduction method.
Mathematics Subject Classification:  65H10, 90C33, 90C30.

Received: March 2009;      Revised: October 2009;      Published: November 2009.