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Euclidean Jordan Algebras and Interior-point Algorithms

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Abstract

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.

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  1. Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556-5683, USA

    Leonid Faybusovich

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  1. Leonid Faybusovich
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Faybusovich, L. Euclidean Jordan Algebras and Interior-point Algorithms. Positivity 1, 331–357 (1997). https://doi.org/10.1023/A:1009701824047

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  • DOI: https://doi.org/10.1023/A:1009701824047

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