Approximation Schemes for Functional Optimization Problems

S. Giulini () and M. Sanguineti ()
Additional contact information
S. Giulini: University of Genoa
M. Sanguineti: University of Genoa

Journal of Optimization Theory and Applications, 2009, vol. 140, issue 1, No 3, 33-54

Abstract: Abstract Approximation schemes for functional optimization problems with admissible solutions dependent on a large number d of variables are investigated. Suboptimal solutions are considered, expressed as linear combinations of n-tuples from a basis set of simple computational units with adjustable parameters. Different choices of basis sets are compared, which allow one to obtain suboptimal solutions using a number n of basis functions that does not grow “fast” with the number d of variables in the admissible decision functions for a fixed desired accuracy. In these cases, one mitigates the “curse of dimensionality,” which often makes unfeasible traditional linear approximation techniques for functional optimization problems, when admissible solutions depend on a large number d of variables.

Keywords: Functional optimization; Approximation schemes; Complexity of admissible solutions; Upper bounds on accuracy; Curse of dimensionality; Ritz method; Extended Ritz method (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-008-9471-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:140:y:2009:i:1:d:10.1007_s10957-008-9471-6

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-008-9471-6

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().