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Computationally Efficient Approximation Schemes for Functional Optimization

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)

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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
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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