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Smoothing techniques in Euclidean Jordan algebras

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  • BAES, Michel

Abstract

We extend the powerful smoothing techniques of Yu. Nesterov to the framework of Euclidean Jordan algebras. This study allows us to design a new scheme for minimizing the largest eigenvalue of an affine function on a Euclidean Jordan algebra. We prove that its complexity is in the order of O(1/ ), where is the absolute tolerance on the value of the objective. Particularizing our result, we propose a new algorithm to minimize a sum of Euclidean norms and we perform its complete complexity analysis.

Suggested Citation

  • BAES, Michel, 2006. "Smoothing techniques in Euclidean Jordan algebras," LIDAM Discussion Papers CORE 2006013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2006013
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2006.html
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    1. BAES, Michel, 2004. "Spectral functions on Jordan algebras : differentiability and convexity properties," LIDAM Discussion Papers CORE 2004016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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