Abstract
We study the linear convergence of a simple pattern search method on non quasi-convex functions on continuous domains. Assumptions include an assumption on the sampling performed by the evolutionary algorithm (supposed to cover efficiently the neighborhood of the current search point), the conditioning of the objective function (so that the probability of improvement is not too low at each time step, given a correct step size), and the unicity of the optimum.
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Acknowledgements
We are grateful to Rémi Bergasse [2] for interesting discussions.
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Decock, J., Teytaud, O. (2014). Linear Convergence of Evolution Strategies with Derandomized Sampling Beyond Quasi-Convex Functions. In: Legrand, P., Corsini, MM., Hao, JK., Monmarché, N., Lutton, E., Schoenauer, M. (eds) Artificial Evolution. EA 2013. Lecture Notes in Computer Science(), vol 8752. Springer, Cham. https://doi.org/10.1007/978-3-319-11683-9_5
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