@article{eprints1705,
            year = {2011},
           title = {Functional optimization by variable-basis approximation schemes},
           pages = {103--106},
          number = {1},
          volume = {9},
          author = {Giorgio Gnecco},
         journal = {4OR: A Quarterly Journal of Operations Research},
       publisher = {Springer},
        keywords = {Optimization, Operations Research/Decision Theory,    Industrial and Production Engineering},
             url = {http://eprints.imtlucca.it/1705/},
        abstract = {This is a summary of the author?s PhD thesis, supervised by Marcello Sanguineti and defended on April 2, 2009 at Universit{\`a} 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 {\ensuremath{\Phi}} 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?spannG{\ensuremath{\Phi}}(f)?inff?S{\ensuremath{\Phi}}(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.}
}