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Superlinear convergence of an algorithm for monotone linear complementarity problems, when no strictly complementary solution exists

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  • Sturm, J.F.

Abstract

A new predictor--corrector interior point algorithm for solving monotone linear complementarity problems (LCP) is proposed, and it is shown to be superlinearly convergent with at least order 1.5, even if the LCP has no strictly complementary solution. Unlike Mizuno's recent algorithm (Mizuno, 1996), the fast local convergence is attained without any need for estimating the optimal partition. In the special case that a strictly complementary solution does exist, the order of convergence becomes quadratic. The proof relies on an investigation of the asymptotic behavior of first and second order derivatives that are associated with trajectories of weighted centers for LCP.

Suggested Citation

  • Sturm, J.F., 1996. "Superlinear convergence of an algorithm for monotone linear complementarity problems, when no strictly complementary solution exists," Econometric Institute Research Papers EI 9656-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1391
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    Cited by:

    1. Josef Stoer & Martin Wechs & Shinji Mizuno, 1998. "High Order Infeasible-Interior-Point Methods for Solving Sufficient Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 832-862, November.

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