%V 145
%I Springer-Verlag
%T Estimates of Variation with Respect to a Set and Applications to Optimization Problems
%P 53-75
%N 1
%R 10.1007/s10957-009-9620-6
%J Journal of Optimization Theory and Applications
%L eprints1714
%D 2010
%X 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.
%K Convex hulls; Variational norms; Radial-basis functions; Functional optimization; Curse of dimensionality; Approximation schemes; Ritz-type methods; Learning from data
%A Giorgio Gnecco
%A Marcello Sanguineti