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Euclidean Jordan algebras and interior-point algorithms. (English) Zbl 0973.90095
Summary: We provide an introduction to the theory of interior-point algorithms of optimization based on the theory of Euclidean Jordan algebras. A short-step path-following algorithm for the convex quadratic problem on the domain, obtained as the intersection of a symmetric cone with an affine subspace, is considered. Connections with the Linear monotone complementarity problem are discussed. Complexity estimates in terms of the rank of the corresponding Jordan algebra are obtained. Necessary results from the theory of Euclidean Jordan algebras are presented.

90C51 Interior-point methods
17C99 Jordan algebras (algebras, triples and pairs)
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