TY  - JOUR
ID  - eprints1693
TI  - Computationally Efficient Approximation Schemes for Functional Optimization
AV  - none
KW  - functional optimization
KW  -  approximation schemes
KW  -  complexity of admissible solutions
KW  -  curse of dimensionality
KW  -  (extended) Ritz method
KW  -  model-based fault diagnosis
KW  -  nonlinear programming
KW  -  stochastic approximation
KW  -  on-line and off-line optimization
UR  - https://www.novapublishers.com/catalog/product_info.php?products_id=20971
IS  - 1/2
VL  - 17
PB  - Nova Publishers
EP  - 189
A1  - Alessandri, Angelo
A1  - Gnecco, Giorgio
A1  - Sanguineti, Marcello
SP  - 153
N2  - 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. 
JF  - International Journal of Computer Research
SN  - 1535-6698
Y1  - 2008///
ER  -