A New Inclusion Function for Optimization: Kite&mdashlThe One Dimensional Case

Authors:
Tamás Vinkó;Jean-Louis Lagouanelle;Tibor Csendes
Affiliations:
Research Group on Artificial Intelligence of the Hungarian Academy of Sciences and, University of Szeged, Szeged, Hungary;Lab. LIMA, Institut de Recherche en Informatique de Toulouse, France;Institute of Informatics, University of Szeged, Szeged, Hungary
Venue:
Journal of Global Optimization
Year:
2004

Citing 10
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ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part III

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Abstract

In this paper the kite inclusion function is presented for branch-and-bound type interval global optimization using at least gradient information. The basic idea comes from the simultaneous usage of the centered forms and the linear boundary value forms. We will show that the new technique is not worse and usually considerably better than these two. The best choice for the center of the kite inclusion will be given. The isotonicity and at least quadratical convergence hold and there is a pruning effect of the kite which is derived from the construction of the inclusion, thus more function evaluations are not needed to use it. A numerical investigation on large standard multiextremal test functions has been done to show the performance.