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Splitting Method for Linear Complementarity Problems
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Splitting Method for Linear Complementarity Problems
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Keywords LCP - Splitting method - SOR method
Splitting methods were originally proposed as a generalization of the classical SOR method for solving a system of linear equations [8,25], and in the late 1970s they were extended to the linear complementarity problem (LCP; cf. Linear complementarity problem) [1,2, Chap. 5], [10,13,18]. These methods are iterative and are best suited for problems in which exploitation of sparsity is important, such as large sparse linear programs and the discretization of certain elliptic boundary value problems with obstacle.
To describe the splitting methods, we formulate the LCP (with bound constraints) as the problem of finding an x = (x 1, …, x n ) ∊ R n solving the following system of nonlinear equations:
where M = [m ij ] i, j = 1, …, n ∊ R n×n , q = (q 1, …, q n ) ∊ R n and the lower bound
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