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    Commutation principles for optimization problems on spectral sets in Euclidean Jordan algebras

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    2009.04874.pdf (139.9Kb)
    Links to Files
    https://arxiv.org/abs/2009.04874
    Permanent Link
    http://hdl.handle.net/11603/20000
    Collections
    • UMBC Faculty Collection
    • UMBC Mathematics and Statistics Department
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    Author/Creator
    Gowda, Muddappa
    Date
    2020-09-10
    Type of Work
    10 pages
    Text
    conference papers and proceedings preprints
    Citation of Original Publication
    Muddappa Gowda, Commutation principles for optimization problems on spectral sets in Euclidean Jordan algebras, https://arxiv.org/abs/2009.04874
    Rights
    This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
    Abstract
    The commutation principle of Ramirez, Seeger, and Sossa proved in the setting of Euclidean Jordan algebras says that when the sum of a real valued function h and a spectral function Φ is minimized/maximized over a spectral set E, any local optimizer a at which h is Fréchet differentiable operator commutes with the derivative h′(a). In this paper, assuming the existence of a subgradient in place the derivative (of h), we establish `strong operator commutativity' relations: If a solves the problem maxE(h+Φ), then a strongly operator commutes with every element in the subdifferential of h at a; If E and h are convex and a solves the problem minEh, then a strongly operator commutes with the negative of some element in the subdifferential of h at a. These results improve known (operator) commutativity relations for linear h and for solutions of variational inequality problems. We establish these results via a geometric commutation principle that is valid not only in Euclidean Jordan algebras, but also in the broader setting of FTvN-systems.


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    Albin O. Kuhn Library & Gallery
    University of Maryland, Baltimore County
    1000 Hilltop Circle
    Baltimore, MD 21250
    www.umbc.edu/scholarworks

    Contact information:
    Email: scholarworks-group@umbc.edu
    Phone: 410-455-3021


    If you wish to submit a copyright complaint or withdrawal request, please email mdsoar-help@umd.edu.