<> "The repository administrator has not yet configured an RDF license."^^ . <> . . . "Functional optimization in OR problems with very large numbers of variables"^^ . "Functional optimization, or \"infinite-dimensional programming\", investigates the minimization (or maximization) of functionals with respect to admissible\r\nsolutions belonging to infinite-dimensional spaces of functions. In OR applications, such functions may express, e.g., \r\n-releasing policies in water-resources management;\r\n-exploration strategies stochastic graphs;\r\n-routing strategies in telecommunication networks;\r\n-input/output mappings in learning from data, etc.\r\nInfinite dimension makes inapplicable many tools used in mathematical programming, and variational methods provide closed-form solutions only in particular cases. Suboptimal solutions can be sought via \"linear approximation\r\nschemes\",i.e., linear combinations of fixed basis functions (e.g., polynomial expansions):\r\nthe functional problem is reduced to optimization of the coefficients\r\nof the linear combinations (\"Ritz method\"). Most often, admissible solutions\r\nare functions dependent on many variables, related, e.g., to\r\n-reservoirs in water-resources management;\r\n-nodes of a communication network;\r\n-items in inventory problems;\r\n-freeway sections in traffic management.\r\nUnfortunately, linear schemes may be computationally inefficient because\r\nof the \"curse of dimensionality\": the number of basis functions, necessary to\r\nobtain a desired accuracy, may grow \"very fast\" with the number of variables.\r\nThis motivates the \"Extended Ritz Method\"(ERIM), based on nonlinear approximation schemes formed by linear combinations of computational units\r\ncontaining \"inner\" parameters which make the schemes nonlinear to be optimized (together with the coefficients of the combinations) via nonlinear programming algorithms. Experimental results show that this approach obtains surprisingly good performances. We present recent theoretical results that give insights into the possibility to cope with the curse of dimensionality in functional optimization via the ERIM, when admissible solutions contain very large numbers of variables."^^ . "2011" . . . . . . . . . . . . . "Marcello"^^ . "Sanguineti"^^ . "Marcello Sanguineti"^^ . . "Giorgio"^^ . "Gnecco"^^ . "Giorgio Gnecco"^^ . . "Riccardo"^^ . "Zoppoli"^^ . "Riccardo Zoppoli"^^ . . . . "AIRO 2011"^^ . . . . . "Brescia, Italy"^^ . . . . . "HTML Summary of #1672 \n\nFunctional optimization in OR problems with very large numbers of variables\n\n" . "text/html" . . . "QA75 Electronic computers. Computer science"@en . .