Abstract
A homogeneous isotropic Gaussian random field is accepted as a statistical model of objective functions, aiming to construct global optimization algorithms. The asymptotic of the conditional mean and variance is considered, assuming that the random field values are known at the vertices of a simplex, and that the latter is contracting. The obtained result theoretically substantiates the construction of the recently proposed bi-variate global optimization algorithm, which arouses interest due to good performance in testing experiments and the established convergence rate. The obtained result also enhances motivation to extend the aforementioned algorithm to higher dimensions.
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Acknowledgements
This research was funded by a grant (No. MIP-051/2014) from the Research Council of Lithuania.
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Žilinskas, A., Gimbutienė, G. (2015). On an Asymptotic Property of a Simplicial Statistical Model of Global Optimization. In: Migdalas, A., Karakitsiou, A. (eds) Optimization, Control, and Applications in the Information Age. Springer Proceedings in Mathematics & Statistics, vol 130. Springer, Cham. https://doi.org/10.1007/978-3-319-18567-5_20
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DOI: https://doi.org/10.1007/978-3-319-18567-5_20
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