relation: http://eprints.imtlucca.it/3123/
title: On the Curse of Dimensionality in the Ritz Method
creator: Gnecco, Giorgio
subject: QA75 Electronic computers. Computer science
description: It is shown that the classical Ritz method of the calculus of variations suffers from the “curse of dimensionality,” i.e., an exponential growth, as a function of the number of variables, of the dimension a linear subspace needs in order to achieve a desired relative improvement in the accuracy of approximation of the optimal solution value. The proof is constructive and is obtained by exhibiting a family of infinite-dimensional optimization problems for which this happens, namely those with quadratic functional and spherical constraint. The results provide a theoretical motivation for the search of alternative solution methods, such as the so-called “extended Ritz method,” to deal with the curse of dimensionality.
publisher: Springer
date: 2016
type: Article
type: PeerReviewed
identifier:   Gnecco, Giorgio  On the Curse of Dimensionality in the Ritz Method.  Journal of Optimization Theory and Applications, 168 (2).  pp. 488-509.  ISSN 0022-3239      (2016)  
relation: http://link.springer.com/article/10.1007%2Fs10957-015-0804-y
relation: 10.1007/s10957-015-0804-y