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New modulus-based matrix splitting methods for implicit complementarity problem. (English) Zbl 1508.65029

Summary: In this paper, based on the published works by Z.-Z. Bai and P.-L. Tong [“Iterative methods for linear complementarity problem”, J. Univ. Electr. Sci. Tech. China 22, 420–424 (1993)] and Z.-Z. Bai and T.-Z. Huang [“Accelerated overrelaxation methods for solving linear complementarity problem”, J. Univ. Electr. Sci. Tech. China 23, 428–432 (1994)], we design a class of new modulus-based matrix splitting methods for solving the implicit complementarity problem (ICP) by a new equivalent fixed-point form of the ICP. Some sufficient conditions to guarantee the convergence of the proposed method are presented. Numerical examples are offered to show the efficiency of the proposed method.

MSC:

65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
65K05 Numerical mathematical programming methods
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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