Predictor-corrector method for linear complementarity problems with polynomial complexity and superlinear convergence

AbstractWe extend the Mizuno-Todd-Ye predictor-corrector algorithm for solving monotone linear complementarity problems. We prove that the extended algorithm is globally Q-linearly convergent and solves problems with integer data of bitlengthL in at most $$O(\sqrt n L)$$ iterations. We also prove that the duality gap converges to zero Q-superlinearly for problems having strictly complementary solutions. Our results generalize the results obtained by Ye, Tapia, and Zhang for linear programming.

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