Abstract
Given ann × n matrixM and ann-dimensional vectorq, the problem of findingn-dimensional vectorsx andy satisfyingy = Mx + q, x ≥ 0,y ≥ 0,x i y i = 0 (i = 1, 2,⋯,n) is known as a linear complementarity problem. Under the assumption thatM is positive semidefinite, this paper presents an algorithm that solves the problem in O(n 3 L) arithmetic operations by tracing the path of centers,{(x, y) ∈ S: x i y i =μ (i = 1, 2,⋯,n) for some μ > 0} of the feasible regionS = {(x, y) ≥ 0:y = Mx + q}, whereL denotes the size of the input data of the problem.
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Kojima, M., Mizuno, S. & Yoshise, A. A polynomial-time algorithm for a class of linear complementarity problems. Mathematical Programming 44, 1–26 (1989). https://doi.org/10.1007/BF01587074
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DOI: https://doi.org/10.1007/BF01587074