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

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

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Article ID: iaor2012627
Volume: 152
Issue: 3
Start Page Number: 739
End Page Number: 772
Publication Date: Mar 2012
Journal: Journal of Optimization Theory and Applications
Authors: ,
Keywords: heuristics
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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