Abstract
We consider the intrinsic difficulty of global optimization in high dimensional Euclidean space. We adopt an asymptotic analysis, and give a lower bound on the number of function evaluations required to obtain a given error tolerance. This lower bound complements upper bounds provided by recently proposed algorithms.
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Acknowledgements
The motivation for this investigation grew out of discussions with A. Žilinskas.
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Calvin, J.M. (2016). On the Asymptotic Tractability of Global Optimization. In: Pardalos, P., Zhigljavsky, A., Žilinskas, J. (eds) Advances in Stochastic and Deterministic Global Optimization. Springer Optimization and Its Applications, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-29975-4_1
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DOI: https://doi.org/10.1007/978-3-319-29975-4_1
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