A NEW POLYNOMIAL INTERIOR-POINT ALGORITHM FOR THE MONOTONE LINEAR COMPLEMENTARITY PROBLEM OVER SYMMETRIC CONES WITH FULL NT-STEPS

G. Q. Wang ()
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G. Q. Wang: College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2012, vol. 29, issue 02, 1-20

Abstract: In this paper, we present a new polynomial interior-point algorithm for the monotone linear complementarity problem over symmetric cones by employing the framework of Euclidean Jordan algebras. At each iteration, we use only full Nesterov and Todd steps. The currently best known iteration bound for small-update method, namely, $O(\sqrt{r}\log{\frac{r}{\varepsilon}})$, is obtained, where r denotes the rank of the associated Euclidean Jordan algebra and ε the desired accuracy.

Keywords: Symmetric cone linear complementarity problem; interior-point algorithm; Euclidean Jordan algebra; small-update method; iteration bound; 90C33; 90C51 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S0217595912500157

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