Approximation Schemes for Functional Optimization Problems |
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Authors: | S Giulini M Sanguineti |
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Institution: | (1) Sciences Department for Architecture (DSA), University of Genoa, Stradone S. Agostino 37, 16123 Genoa, Italy;(2) Department of Communications, Computer, and System Sciences (DIST), University of Genoa, Via Opera Pia 13, 16145 Genoa, Italy |
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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 of simple computational units with adjustable parameters. Different choices of basis sets are compared,
which allow one to obtain suboptimal solutions using a number n of basis functions that does not grow “fast” with the number d of variables in the admissible decision functions for a fixed desired accuracy. In these cases, one mitigates the “curse
of dimensionality,” which often makes unfeasible traditional linear approximation techniques for functional optimization problems,
when admissible solutions depend on a large number d of variables.
Marcello Sanguineti was partially supported by a PRIN grant from the Italian Ministry for University and Research (project
“Models and Algorithms for Robust Network Optimization”). |
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Keywords: | Functional optimization Approximation schemes Complexity of admissible solutions Upper bounds on accuracy Curse of dimensionality Ritz method Extended Ritz method |
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