A new type of solution method for the generalized linear complementarity problem over a polyhedral cone

This paper addresses the generalized linear complementarity problem (GLCP) over a polyhedral cone. To solve the problem, we first equivalently convert the problem into an affine variational inequalities problem over a closed polyhedral cone, and then propose a new type of method to solve the GLCP based on the error bound estimation. The global and R-linear convergence rate is established. The numerical experiments show the efficiency of the method. This work was supported by National Natural Science Foundation of China (No. 10771120). Hong-Chun Sun received the B. Sc. degree in mathematics from Qufu Normal University (QNU), PRC, in 1990, and the M. Sc. degree in operations and cybernetics from QNU in 2005. Currently, he is an associated professor in the Department of Mathematics at Linyi Normal University, PRC. His research interests include nonlinear optimization. Yan-Liang Dong received the B. Sc. degree in mathematics from Shandong Normal University, PRC, in 2003. He is currently a master student in operations and cybernetics from Qufu Normal University, PRC. His research interests include algorithm for nonlinear programming.