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A Class of Polynomial Interior Point Algorithms for the Cartesian P-Matrix Linear Complementarity Problem over Symmetric Cones

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Abstract

In this paper, we present a new class of polynomial interior point algorithms for the Cartesian P-matrix linear complementarity problem over symmetric cones based on a parametric kernel function, which determines both search directions and the proximity measure between the iterate and the center path. The symmetrization of the search directions used in this paper is based on the Nesterov and Todd scaling scheme. By using Euclidean Jordan algebras, we derive the iteration bounds that match the currently best known iteration bounds for large- and small-update methods.

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Authors and Affiliations

  1. College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai, 201620, China

    G. Q. Wang

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Y. Q. Bai

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  1. G. Q. Wang
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  2. Y. Q. Bai
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Correspondence to G. Q. Wang.

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Communicated by Florian A. Potra.

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Wang, G.Q., Bai, Y.Q. A Class of Polynomial Interior Point Algorithms for the Cartesian P-Matrix Linear Complementarity Problem over Symmetric Cones. J Optim Theory Appl 152, 739–772 (2012). https://doi.org/10.1007/s10957-011-9938-8

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