Empirical Investigation of the Convergence Speed of Inclusion Functions in a Global Optimization Context

Empirical Investigation of the Convergence Speed of Inclusion Functions in a Global Optimization... This paper deals with the empirical convergence speed of inclusion functions applied in interval methods for global optimization. According to our experience the natural interval extension of a given function can be as good as a usual quadratically convergent inclusion function, and although centered forms are in general only of second-order, they can perform as one of larger convergence order. These facts indicate that the theoretical convergence order should not be the only indicator of the quality of an inclusion function, it would be better to know which inclusion function can be used most efficiently in concrete instances. For this reason we have investigated the empirical convergence speed of the usual inclusion functions on some test functions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Empirical Investigation of the Convergence Speed of Inclusion Functions in a Global Optimization Context

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2005 by Springer Science + Business Media, Inc.
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1007/s11155-005-6890-z
Publisher site
See Article on Publisher Site

Abstract

This paper deals with the empirical convergence speed of inclusion functions applied in interval methods for global optimization. According to our experience the natural interval extension of a given function can be as good as a usual quadratically convergent inclusion function, and although centered forms are in general only of second-order, they can perform as one of larger convergence order. These facts indicate that the theoretical convergence order should not be the only indicator of the quality of an inclusion function, it would be better to know which inclusion function can be used most efficiently in concrete instances. For this reason we have investigated the empirical convergence speed of the usual inclusion functions on some test functions.

Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2005

References

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