eprintid: 1705
rev_number: 6
eprint_status: archive
userid: 46
dir: disk0/00/00/17/05
datestamp: 2013-09-12 13:38:20
lastmod: 2013-09-16 12:03:00
status_changed: 2013-09-12 13:38:20
type: article
metadata_visibility: no_search
creators_name: Gnecco, Giorgio
creators_id: giorgio.gnecco@imtlucca.it
title: Functional optimization by variable-basis approximation schemes
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
keywords: Optimization, Operations Research/Decision Theory,    Industrial and Production Engineering
abstract: 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.
date: 2011
date_type: published
publication: 4OR: A Quarterly Journal of Operations Research
volume: 9
number: 1
publisher: Springer
pagerange: 103-106
id_number: 10.1007/s10288-010-0134-8
refereed: TRUE
issn: 1619-4500
official_url: http://dx.doi.org/10.1007/s10288-010-0134-8
citation:   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)