1 Jordan algebras and symmetric cones

In this paper, we present a predictor–corrector infeasible-interior-point method based on a new wide neighborhood of the central path for linear complementarity problem over symmetric cones (SCLCP) with the Cartesian [Formula: see text]-property. The convergence of the algorithm is proved for commutative class of search directions. Moreover, using the theory of Euclidean Jordan algebras and some elegant tools, the iteration bound improves the earlier complexity of these kind of algorithms for the Cartesian [Formula: see text]-SCLCPs.

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Infinite dimensional Jordan algebras and symmetric cones

Journal of Algebra ◽

10.1016/j.jalgebra.2017.08.017 ◽

2017 ◽

Vol 491 ◽

pp. 357-371 ◽

Cited By ~ 4

Author(s):

Cho-Ho Chu

Keyword(s):

Jordan Algebras ◽

Symmetric Cones ◽

Infinite Dimensional

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Jordan Algebras and Dual Affine Connections on Symmetric Cones

Positivity ◽

10.1007/s11117-004-7400-y ◽

2004 ◽

Vol 8 (4) ◽

pp. 369-378 ◽

Cited By ~ 4

Author(s):

Keiko Uohashi ◽

Atsumi Ohara

Keyword(s):

Jordan Algebras ◽

Symmetric Cones ◽

Affine Connections ◽

Dual Affine

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

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595912500157 ◽

2012 ◽

Vol 29 (02) ◽

pp. 1250015 ◽

Cited By ~ 9

Author(s):

G. Q. WANG

Keyword(s):

Linear Complementarity Problem ◽

Interior Point ◽

Complementarity Problem ◽

Euclidean Jordan Algebra ◽

Linear Complementarity ◽

Jordan Algebras ◽

Symmetric Cones ◽

Interior Point Algorithm ◽

Euclidean Jordan Algebras ◽

Iteration Bound

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, [Formula: see text], is obtained, where r denotes the rank of the associated Euclidean Jordan algebra and ε the desired accuracy.

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