%0 Journal Article
%@ 1619-4500
%A Gnecco, Giorgio
%D 2011
%F eprints:1705
%I Springer
%J 4OR: A Quarterly Journal of Operations Research
%K Optimization, Operations Research/Decision Theory,    Industrial and Production Engineering
%N 1
%P 103-106
%T Functional optimization by variable-basis approximation schemes
%U http://eprints.imtlucca.it/1705/
%V 9
%X 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.