scholarly journals Infinite dimensional Jordan algebras and symmetric cones

2017 ◽  
Vol 491 ◽  
pp. 357-371 ◽  
Author(s):  
Cho-Ho Chu
Keyword(s):  
Jordan Algebras ◽  
Symmetric Cones ◽  
Infinite Dimensional

scholarly journals Representations in L2-Spaces on Infinite-Dimensional Symmetric Cones

2002 ◽  
Vol 190 (1) ◽  
pp. 133-178 ◽  
Author(s):  
Karl-Hermann Neeb ◽  
Bent Ørsted
Keyword(s):  
Symmetric Cones ◽  
Infinite Dimensional

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.

Hilbert space methods in the theory of Jordan algebras. I

1975 ◽  
Vol 78 (2) ◽  
pp. 293-300 ◽  
Author(s):  
C. Viola Devapakkiam
Keyword(s):  
Hilbert Space ◽  
Classification Problem ◽  
Jordan Algebras ◽  
Inner Product ◽  
Uniqueness Problem ◽  
Associative Algebras ◽  
Infinite Dimensional

In this paper, we study the structure of certain infinite-dimensional Jordan algebras admitting an inner product. These algebras, called J*-algebras in the sequel, have already been considered in (4) in connexion with the norm uniqueness problem for non-associative algebras. We deal here with the structure and classification of these algebras. Existence of self-adjoint idempotents plays a central role in the classification problem.

Jordan Algebras and Dual Affine Connections on Symmetric Cones

Positivity ◽  
2004 ◽  
Vol 8 (4) ◽  
pp. 369-378 ◽  
Author(s):  
Keiko Uohashi ◽  
Atsumi Ohara
Keyword(s):  
Jordan Algebras ◽  
Symmetric Cones ◽  
Affine Connections ◽  
Dual Affine

scholarly journals On Pre-Hilbert Noncommutative Jordan Algebras Satisfying

ISRN Algebra ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Mohamed Benslimane ◽  
Abdelhadi Moutassim
Keyword(s):  
Vector Space ◽  
Associative Algebra ◽  
Jordan Algebra ◽  
Alternative Algebra ◽  
Jordan Algebras ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
First Case ◽  
Hilbert Norm ◽  
Complex Powers

Let be a real or complex algebra. Assuming that a vector space is endowed with a pre-Hilbert norm satisfying for all . We prove that is finite dimensional in the following cases. (1) is a real weakly alternative algebra without divisors of zero. (2) is a complex powers associative algebra. (3) is a complex flexible algebraic algebra. (4) is a complex Jordan algebra. In the first case is isomorphic to or and is isomorphic to in the last three cases. These last cases permit us to show that if is a complex pre-Hilbert noncommutative Jordan algebra satisfying for all , then is finite dimensional and is isomorphic to . Moreover, we give an example of an infinite-dimensional real pre-Hilbert Jordan algebra with divisors of zero and satisfying for all .

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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