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Functional optimization by variable-basis approximation schemes

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)

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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.

Item Type: Article
Identification Number: 10.1007/s10288-010-0134-8
Uncontrolled Keywords: Optimization, Operations Research/Decision Theory, Industrial and Production Engineering
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Giorgio Gnecco
Date Deposited: 12 Sep 2013 13:38
Last Modified: 16 Sep 2013 12:03
URI: http://eprints.imtlucca.it/id/eprint/1705

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