Polynomial complexity of an interior point algorithm with a second order corrector step for symmetric cone programming

Jian Zhang () and Kecun Zhang ()

Mathematical Methods of Operations Research, 2011, vol. 73, issue 1, 75-90

Abstract: In this paper, we propose a second order interior point algorithm for symmetric cone programming using a wide neighborhood of the central path. The convergence is shown for commutative class of search directions. The complexity bound is $${O(r^{3/2}\,\log\epsilon^{-1})}$$ for the NT methods, and $${O(r^{2}\,\log\epsilon^{-1})}$$ for the XS and SX methods, where r is the rank of the associated Euclidean Jordan algebra and $${\epsilon\,{ > }\,0}$$ is a given tolerance. If the staring point is strictly feasible, then the corresponding bounds can be reduced by a factor of r 3/4 . The theory of Euclidean Jordan algebras is a basic tool in our analysis. Copyright Springer-Verlag 2011

Keywords: Linear programming; Symmetric cone; Euclidean Jordan algebra; Interior point method; Polynomial complexity; 90C05; 90C25; 90C51 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s00186-010-0334-1

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