Abstract
The purpose of this paper is to present a new polynomial time method for a linear complementarity problem with a positive semi-definite matrix. The method follows a sequence of points. If we generate the sequence on a path, we can construct a path following method, and if we generate the sequence based on a potential function, we can construct a potential reduction method. The method has the advantage that it requires at most\(O(\sqrt n L)\) iterations for any initial feasible point whose components lie between 2−O(L) and 2O(L).
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Research was supported in part by Grant-in-Aids for Encouragement of Young Scientists (63730014) and for General Scientific Research (63490010) of The Ministry of Education, Science and Culture.
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Mizuno, S. A new polynomial time method for a linear complementarity problem. Mathematical Programming 56, 31–43 (1992). https://doi.org/10.1007/BF01580891
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DOI: https://doi.org/10.1007/BF01580891