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)
Full text not available from this repository.Abstract
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.
| Item Type: | Article |
|---|---|
| Identification Number: | https://doi.org/10.1007/s10957-015-0804-y |
| Additional Information: | First online: 03 September 2015 |
| Uncontrolled Keywords: | Ritz method; Curse of dimensionality; Infinite-dimensional optimization; Approximation schemes; Extended Ritz method |
| Subjects: | Q Science > QA Mathematics > QA75 Electronic computers. Computer science |
| Research Area: | Computer Science and Applications |
| Depositing User: | Caterina Tangheroni |
| Date Deposited: | 26 Feb 2016 12:39 |
| Last Modified: | 26 Feb 2016 12:39 |
| URI: | http://eprints.imtlucca.it/id/eprint/3123 |
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