Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method

Cambridge university press, Cambridge (2004)

Boyd, S., Vandenberghe, L.: Convex Optimization · 2004

Earlier work this paper cites.

Math. Program. 108

Nesterov, Y., Polyak, B.T.: Cubic regularization of Newton’s method and its global performance · 2006

Earlier work this paper cites.

Optim. Methods Softw. 22

Nesterov, Y.: Modified Gauss–Newton scheme with worst case guarantees for global performance · 2007

Earlier work this paper cites.

Math. Program. 112

Nesterov, Y.: Accelerating the cubic regularization of Newton’s method on convex problems · 2008

Earlier work this paper cites.

Math. Program. 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

Earlier work this paper cites.

Math. Program. 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.

Optim. Methods Softw. 27

Cartis, C., Gould, N.I., Toint, P.L.: Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization · 2012

Cited alongside, same era.

arXiv:1612.00547 (2016)

Original

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 49th Annual ACM SIGACT Symposium on Theory of Computing, pp. 1195–1199. ACM (2017)

Agarwal, N., Allen-Zhu, Z., Bullins, B., Hazan, E., Ma, T.: Finding approximate local minima faster than gradient descent · 2017

Cited alongside, same era.

arXiv:1710.05782 (2017)

Original

Ghadimi, S., Liu, H., Zhang, T.: Second-order methods with cubic regularization under inexact information · 2017

Cited alongside, same era.

SIAM J. Optim. 27

Grapiglia, G.N., Nesterov, Y.: Regularized Newton methods for minimizing functions with Hölder continuous Hessians · 2017

Cited alongside, same era.

Math. Program. 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., Richtárik, P.: Randomized block cubic Newton method · 2018

Later among the works it cites.

Springer, Berlin (2018)

Nesterov, Y.: Lectures on Convex Optimization, vol. 137 · 2018

Later among the works it cites.

In: Advances in Neural Information Processing Systems, pp. 2899–2908 (2018)

Tripuraneni, N., Stern, M., Jin, C., Regier, J., Jordan, M.I.: Stochastic cubic regularization for fast nonconvex optimization · 2018

Later among the works it cites.

SIAM J. Optim. 29

Grapiglia, G.N., Nesterov, Y.: Accelerated regularized Newton methods for minimizing composite convex functions · 2019

Closest in time.

In: Mathematical Programming pp. 1–27 (2019)

Nesterov, Y.: Implementable tensor methods in unconstrained convex optimization · 2019