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Superlinear primal-dual affine scaling algorithms for LCP

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Abstract

We describe an interior-point algorithm for monotone linear complementarity problems in which primal-dual affine scaling is used to generate the search directions. The algorithm is shown to have global and superlinear convergence with Q-order up to (but not including) two. The technique is shown to be consistent with a potential-reduction algorithm, yielding the first potential-reduction algorithm that is both globally and superlinearly convergent.

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Corresponding author. The work of this author was based on research supported by the Office of Scientific Computing, U.S. Department of Energy, under Contract W-31-109-Eng-38.

The work of this author was based on research supported by the National Science Foundation under grant DDM-9109404 and the Office of Naval Research under grant N00014-93-1-0234. This work was done while the author was a faculty member of the Systems and Industrial Engineering Department at the University of Arizona.

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Monteiro, R.D.C., Wright, S.J. Superlinear primal-dual affine scaling algorithms for LCP. Mathematical Programming 69, 311–333 (1995). https://doi.org/10.1007/BF01585562

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  • DOI: https://doi.org/10.1007/BF01585562

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