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Convergence of iterates of an inexact matrix splitting algorithm for the symmetric monotone linear complementarity problem. (English) Zbl 0777.90070

Summary: Convergence of iterates is established for a symmetric regular matrix splitting algorithm for the solution of the symmetric monotone linear complementarity problem where the subproblems are solved inexactly. The notable iterate convergence recently established by Z.-Q. Luo and P. Tseng [SIAM J. Control Optimization 29, No. 5, 1037-1060 (1991; Zbl 0734.90101)] for exact subproblem solution is extended here to inexact subproblem solution for a symmetric matrix splitting. A principal application of the present result is to iterate convergence for the inexact block Jacobi method for which J.-S. Pang and J.-M. Yang [Ann. Oper. Res. 14, No. 1-4, 61-75 (1988; Zbl 0753.90065)] established convergence of a subsequence of the iterates.

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C20 Quadratic programming
90-08 Computational methods for problems pertaining to operations research and mathematical programming
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