The global linear convergence of a non--interior path--following algorithm for linear complementarity problems

Jim Burke and Song Xu

A non--interior path following algorithm is proposed for the linear complementarity problem. The method employs smoothing techniques introduced by Kanzow. Under suitable hypotheses, the algorithm is shown to be globally linearly convergent. As with interior point path following methods, the convergence theory relies on the notion of a neighborhood for the central path. However, the choice of neighborhood differs significantly from that which appears in the interior point literature. Numerical experiments are presented that illustrate the significance of the neighborhood concept for non--interior path following algorithms.

Technical report, Department of Mathematics, University of Washington, Seattle, WA 98195, December 1996

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