Associative and Jordan Algebras, and Polynomial Time Interior-Point Algorithms for Symmetric Cones

2001 ◽  
Vol 26 (3) ◽  
pp. 543-564 ◽  
Author(s):  
S. H. Schmieta ◽  
F. Alizadeh
Keyword(s):  
Polynomial Time ◽  
Interior Point ◽  
Jordan Algebras ◽  
Symmetric Cones ◽  
Interior Point Algorithms

A wide neighborhood predictor–corrector infeasible-interior-point method for Cartesian P∗(κ)-LCP over symmetric cones

2016 ◽  
Vol 09 (03) ◽  
pp. 1650049 ◽  
Author(s):  
Marzieh Sayadi Shahraki ◽  
Maryam Zangiabadi ◽  
Hossein Mansouri
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Jordan Algebras ◽  
Point Method ◽  
Symmetric Cones ◽  
Wide Neighborhood ◽  
Euclidean Jordan Algebras ◽  
Iteration Bound ◽  
Infeasible Interior Point Method ◽  
Predictor Corrector

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.

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

2012 ◽  
Vol 29 (02) ◽  
pp. 1250015 ◽  
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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