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In this paper, we study derivatives of powers of Euclidean norm.
Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet 3
Vladimirov, A., Nesterov, Y.E., Chekanov, Y.N.: On uniformly convex functionals · 1978
Earlier work this paper cites.
SIAM Journal on Optimization 1
Schnabel, R.B., Chow, T.T.: Tensor methods for unconstrained optimization using second derivatives · 1991
Earlier work this paper cites.
SIAM (1994)
Nesterov, Y., Nemirovskii, A.: Interior-point polynomial algorithms in convex programming, vol. 13 · 1994
Earlier work this paper cites.
Mathematical Programming 108
Nesterov, Y., Polyak, B.T.: Cubic regularization of Newton method and its global performance · 2006
Earlier work this paper cites.
Mathematical Programming 112
Nesterov, Y.: Accelerating the cubic regularization of Newton’s method on convex problems · 2008
Earlier work this paper cites.
Optimization Online (2009)
Baes, M.: Estimate sequence methods: extensions and approximations · 2009
Earlier work this paper cites.
Mathematical Programming 127
Cartis, C., Gould, N.I., Toint, P.L.: Adaptive cubic regularisation methods for unconstrained optimization. Part I: Motivation, convergence and numerical results · 2011
Earlier work this paper cites.
Mathematical programming 130
Cartis, C., Gould, N.I., Toint, P.L.: Adaptive cubic regularisation methods for unconstrained optimization. Part II: Worst-case function-and derivative-evaluation complexity · 2011
Cited alongside, same era.
Tech. rep., CORE Discussion Paper, Université Catholique de Louvain, Belgium (2015)
Nesterov, Y.: Implementable tensor methods in unconstrained convex optimization · 2015
Cited alongside, same era.
Mathematical Programming 152
Nesterov, Y.: Universal gradient methods for convex optimization problems · 2015
Cited alongside, same era.
arXiv preprint arXiv:1612.00547 (2016)
Carmon, Y., Duchi, J.C.: Gradient descent efficiently finds the cubic-regularized non-convex Newton step · 2016
Cited alongside, same era.
In: Proceedings of the 34th International Conference on Machine Learning-Volume 70, pp. 1895–1904. JMLR (2017)
Kohler, J.M., Lucchi, A.: Sub-sampled cubic regularization for non-convex optimization · 2017
Cited alongside, same era.
SIAM Journal on Optimization 27
Grapiglia, G.N., Nesterov, Y.: Regularized Newton methods for minimizing functions with Hölder continuous Hessians · 2017
Later among the works it cites.
Mathematical Programming 169
Cartis, C., Scheinberg, K.: Global convergence rate analysis of unconstrained optimization methods based on probabilistic models · 2018
Later among the works it cites.
In: International Conference on Machine Learning, pp. 1289–1297 (2018)
Doikov, N., Richtarik, P., et al.: Randomized block cubic Newton method · 2018
Later among the works it cites.
In: Conference on Learning Theory, pp. 1392–1393 (2019)
Gasnikov, A., Dvurechensky, P., Gorbunov, E., Vorontsova, E., Selikhanovych, D., Uribe, C.A., Jiang, B., Wang, H., Zhang, S., Bubeck, S., et al.: Near optimal methods for minimizing convex functions with Lipschitz p p -th derivatives · 2019
Closest in time.
arXiv preprint arXiv:1904.12559 (2019)
Grapiglia, G.N., Nesterov, Y.: Tensor methods for minimizing functions with Hölder continuous higher-order derivatives · 2019
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Cartis, C., Gould, N.I., Toint, P.L.: Improved second-order evaluation complexity for unconstrained nonlinear optimization using high-order regularized models · 2017
Cited alongside, same era.
arXiv preprint arXiv:1905.02671 (2019)
Doikov, N., Nesterov, Y.: Minimizing uniformly convex functions by cubic regularization of Newton method · 2019
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