Alessandri, Angelo and Gnecco, Giorgio and Sanguineti, Marcello
*Computationally Efficient Approximation Schemes for Functional Optimization.*
International Journal of Computer Research, 17 (1/2).
pp. 153-189.
ISSN 1535-6698
(2008)

## 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.

Item Type: | Article |
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Uncontrolled 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 |

Subjects: | Q Science > QA Mathematics > QA75 Electronic computers. Computer science |

Research Area: | Computer Science and Applications |

Depositing User: | Giorgio Gnecco |

Date Deposited: | 12 Sep 2013 10:45 |

Last Modified: | 16 Sep 2013 12:03 |

URI: | http://eprints.imtlucca.it/id/eprint/1693 |

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