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Estimates of Variation with Respect to a Set and Applications to Optimization Problems

Author

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  • G. Gnecco

    (University of Genoa
    University of Genoa)

  • M. Sanguineti

    (University of Genoa)

Abstract

A variational norm that plays a role in functional optimization and learning from data is investigated. For sets of functions obtained by varying some parameters in fixed-structure computational units (e.g., Gaussians with variable centers and widths), upper bounds on the variational norms associated with such units are derived. The results are applied to functional optimization problems arising in nonlinear approximation by variable-basis functions and in learning from data. They are also applied to the construction of minimizing sequences by an extension of the Ritz method.

Suggested Citation

  • G. Gnecco & M. Sanguineti, 2010. "Estimates of Variation with Respect to a Set and Applications to Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 53-75, April.
    • Handle: RePEc:spr:joptap:v:145:y:2010:i:1:d:10.1007_s10957-009-9620-6
    DOI: 10.1007/s10957-009-9620-6
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    References listed on IDEAS

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    1. R. Zoppoli & M. Sanguineti & T. Parisini, 2002. "Approximating Networks and Extended Ritz Method for the Solution of Functional Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 403-440, February.
    2. Vēra Kůrková & Marcello Sanguineti, 2008. "Approximate Minimization of the Regularized Expected Error over Kernel Models," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 747-756, August.
    3. S. Giulini & M. Sanguineti, 2009. "Approximation Schemes for Functional Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 33-54, January.
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    Cited by:

    1. Giorgio Gnecco, 2016. "On the Curse of Dimensionality in the Ritz Method," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 488-509, February.

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