eprintid: 1714
rev_number: 7
eprint_status: archive
userid: 46
dir: disk0/00/00/17/14
datestamp: 2013-09-13 10:27:37
lastmod: 2013-09-16 12:03:00
status_changed: 2013-09-13 10:27:37
type: article
metadata_visibility: show
creators_name: Gnecco, Giorgio
creators_name: Sanguineti, Marcello
creators_id: giorgio.gnecco@imtlucca.it
creators_id: 
title: Estimates of Variation with Respect to a Set and Applications to Optimization Problems
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
keywords: Convex hulls; Variational norms; Radial-basis functions; Functional optimization; Curse of dimensionality; Approximation schemes; Ritz-type methods; Learning from data
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.
date: 2010
date_type: published
publication: Journal of Optimization Theory and Applications
volume: 145
number: 1
publisher: Springer-Verlag
pagerange: 53-75
id_number: 10.1007/s10957-009-9620-6
refereed: TRUE
issn: 0022-3239
official_url: http://dx.doi.org/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”
citation:   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)