@article{eprints1693,
       publisher = {Nova Publishers},
           pages = {153--189},
           title = {Computationally Efficient Approximation Schemes for Functional Optimization},
         journal = {International Journal of Computer Research},
            year = {2008},
          author = {Angelo Alessandri and Giorgio Gnecco and Marcello Sanguineti},
          volume = {17},
          number = {1/2},
             url = {http://eprints.imtlucca.it/1693/},
        keywords = {functional optimization, approximation schemes, complexity of admissible solutions, curse of dimensionality, (extended) Ritz method, model-based fault diagnosis, nonlinear programming, stochastic approximation, on-line and off-line optimization},
        abstract = {Approximation schemes for functional optimization problems with admissible solutions dependent on a large number d of variables are investigated. Suboptimal solutions
are considered, expressed as linear combinations of n-tuples from a basis set. The uses of fixed-basis and variable-basis approximation are compared. In the latter,
simple computational units with adjustable parameters are exploited. Conditions are discussed, under which the number n of basis functions required to guarantee a desired accuracy does not grow ?fast? with the number d of variables in admissible solutions, thus mitigating the ?curse of dimensionality?. As an example of application,
an optimization-based approach to fault diagnosis for nonlinear stochastic systems is presented. Numerical results for a complex instance of the fault-diagnosis problem are given. }
}