relation: http://eprints.imtlucca.it/1705/
title: Functional optimization by variable-basis approximation schemes
creator: Gnecco, Giorgio
subject: QA75 Electronic computers. Computer science
description: This is a summary of the author’s PhD thesis, supervised by Marcello Sanguineti and defended on April 2, 2009 at Università degli Studi di Genova. The thesis is written in English and a copy is available from the author upon request. Functional optimization problems arising in Operations Research are investigated. In such problems, a cost functional Φ has to be minimized over an admissible set S of d-variable functions. As, in general, closed-form solutions cannot be derived, suboptimal solutions are searched for, having the form of variable-basis functions, i.e., elements of the set span n   G of linear combinations of at most n elements from a set G of computational units. Upper bounds on inff∈S∩spannGΦ(f)−inff∈SΦ(f) are obtained. Conditions are derived, under which the estimates do not exhibit the so-called “curse of dimensionality” in the number n of computational units, when the number d of variables grows. The problems considered include dynamic optimization, team optimization, and supervised learning from data.
publisher: Springer
date: 2011
type: Article
type: PeerReviewed
identifier:   Gnecco, Giorgio  Functional optimization by variable-basis approximation schemes.  4OR: A Quarterly Journal of Operations Research, 9 (1).  pp. 103-106.  ISSN 1619-4500      (2011)  
relation: http://dx.doi.org/10.1007/s10288-010-0134-8
relation: 10.1007/s10288-010-0134-8