Abstract
We give a bound on the distance between an arbitrary point and the solution set of a monotone linear complementarity problem in terms of a condition constant that depends on the problem data only and a residual function of the violations of the complementary problem conditions by the point considered. When the point satisfies the linear inequalities of the complementarity problem, the residual consists of the complementarity condition plus its square root. This latter term is essential and without it the error bound cannot hold. We also show that another natural residual that has been employed to bound errors for strictly monotone linear complementarity problems fails to bound errors for the monotone case considered here.
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Sponsored by the United States Army under contract No. DAAG29-80-C-0041. This material is based on research sponsored by National Foundation Grant DCR-8420963 and Air Force Office of Scientific Research Grant AFOSR-ISSA-85-00080.
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Mangasarian, O.L., Shiau, T.H. Error bounds for monotone linear complementarity problems. Mathematical Programming 36, 81–89 (1986). https://doi.org/10.1007/BF02591991
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DOI: https://doi.org/10.1007/BF02591991