%0 Journal Article
%@ 1535-6698
%A Alessandri, Angelo
%A Gnecco, Giorgio
%A Sanguineti, Marcello
%D 2008
%F eprints:1693
%I Nova Publishers
%J International Journal of Computer Research
%K 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
%N 1/2
%P 153-189
%T Computationally Efficient Approximation Schemes for Functional Optimization
%U http://eprints.imtlucca.it/1693/
%V 17
%X 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.