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Regularized learning in Banach spaces as an optimization problem: representer theorems


  • Haizhang Zhang


  • Jun Zhang



We view regularized learning of a function in a Banach space from its finite samples as an optimization problem. Within the framework of reproducing kernel Banach spaces, we prove the representer theorem for the minimizer of regularized learning schemes with a general loss function and a nondecreasing regularizer. When the loss function and the regularizer are differentiable, a characterization equation for the minimizer is also established. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Haizhang Zhang & Jun Zhang, 2012. "Regularized learning in Banach spaces as an optimization problem: representer theorems," Journal of Global Optimization, Springer, vol. 54(2), pages 235-250, October.
  • Handle: RePEc:spr:jglopt:v:54:y:2012:i:2:p:235-250 DOI: 10.1007/s10898-010-9575-z

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    References listed on IDEAS

    1. Loiola, Eliane Maria & de Abreu, Nair Maria Maia & Boaventura-Netto, Paulo Oswaldo & Hahn, Peter & Querido, Tania, 2007. "A survey for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 176(2), pages 657-690, January.
    2. Pierre Chardaire & Alain Sutter, 1995. "A Decomposition Method for Quadratic Zero-One Programming," Management Science, INFORMS, vol. 41(4), pages 704-712, April.
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