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Finding the global minimum of non-convex functions is one of the main and most difficult problems in modern optimization.
Polyak, B.T.: Introduction to optimization. optimization software. Inc., Publications Division, New York 1
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Zhigljavsky, A., Zilinskas, A.: Stochastic Global Optimization, vol. 9 (01 2008). https://doi.org/10.1007/978-0-387-74740-8
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Shor, N.Z.: Minimization methods for non-differentiable functions, vol. 3. Springer Science & Business Media (2012)
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Singer, Y., Vondrak, J.: Information-theoretic lower bounds for convex optimization with erroneous oracles. In: Cortes, C., Lawrence, N.D., Lee, D.D., Sugiyama, M., Garnett, R. (eds.) Advances in Neural Information Processing Systems 28, pp. 3204–3212. Curran Associates, Inc. (2015), http://papers.nips.cc/paper/5841-information-theoretic-lower-bounds-for-convex-optimization-with-erroneous-oracles.pdf
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Risteski, A., Li, Y.: Algorithms and matching lower bounds for approximately-convex optimization. In: Lee, D., Sugiyama, M., Luxburg, U., Guyon, I., Garnett, R. (eds.) Advances in Neural Information Processing Systems. vol. 29. Curran Associates, Inc. (2016), https://proceedings.neurips.cc/paper/2016/file/186fb23a33995d91ce3c2212189178c8-Paper.pdf
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Gasnikov, A.V., Krymova, E.A., Lagunovskaya, A.A., Usmanova, I.N., Fedorenko, F.A.: Stochastic online optimization. single-point and multi-point non-linear multi-armed bandits. convex and strongly-convex case. Automation and remote control 78
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Nesterov, Y., Spokoiny, V.G.: Random gradient-free minimization of convex functions. Foundations of Computational Mathematics 17
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Shamir, O.: An optimal algorithm for bandit and zero-order convex optimization with two-point feedback. Journal of Machine Learning Research 18
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2019
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Boyd, S.P., Vandenberghe, L.: Convex optimization. Cambridge University Press (2018)
2018
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2021
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