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

Gnecco, Giorgio and Sanguineti, Marcello Estimates of Variation with Respect to a Set and Applications to Optimization Problems. Journal of Optimization Theory and Applications, 145 (1). pp. 53-75. ISSN 0022-3239 (2010)

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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.

Item Type: Article
Identification Number: 10.1007/s10957-009-9620-6
Projects: Partially supported by a grant “Progetti di Ricerca di Ateneo 2008” of the University of Genova, project “Solution of Functional Optimization Problems by Nonlinear Approximators and Learning from Data”
Uncontrolled Keywords: Convex hulls; Variational norms; Radial-basis functions; Functional optimization; Curse of dimensionality; Approximation schemes; Ritz-type methods; Learning from data
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Giorgio Gnecco
Date Deposited: 13 Sep 2013 10:27
Last Modified: 16 Sep 2013 12:03
URI: http://eprints.imtlucca.it/id/eprint/1714

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