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A potential reduction method for the generalized linear complementarity problem over a polyhedral cone. (English) Zbl 1187.90296
Summary: 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.
MSC:
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
90C30Nonlinear programming
65H10Systems of nonlinear equations (numerical methods)