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

G. Q. Wang () and Y. Q. Bai ()
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G. Q. Wang: Shanghai University of Engineering Science
Y. Q. Bai: Shanghai University

Journal of Optimization Theory and Applications, 2012, vol. 152, issue 3, No 11, 739-772

Abstract: 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.

Keywords: Symmetric cone linear complementarity problem; Euclidean Jordan algebra; Kernel function; Interior point method; Large- and small-update methods (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-011-9938-8

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