Tensor Methods for Minimizing Convex Functions with H\"{o}lder Continuous Higher-Order Derivatives

S. Banach: Über homogene Polynome in (L2). Studia Math. 7

1938

Earlier work this paper cites.

A. Nemirovskii, D. Yudin.: Problem complexity and method efficiency in optimization. John Wiley & Sons, New York (1983)

1983

Earlier work this paper cites.

Schnabel, R.B., Chow, T.: Tensor methods for unconstrained optimization using second derivatives. SIAM Journal on Optimization 1

1991

Earlier work this paper cites.

Bouaricha, A.: Tensor methods for large, sparse unconstrained optimization. SIAM Journal on Optimization 7

1997

Earlier work this paper cites.

Nesterov, Yu, Polyak, B.T.: Cubic regularization of Newton method and its global performance. Mathematical Programming 108

2006

Earlier work this paper cites.

Nesterov, Yu.: Accelerating the cubic regularization of Newton’s method on convex problems. Mathematical Programming 112

2008

Earlier work this paper cites.

M. Baes: Estimate Sequence Methods: Extensions and Approximations. Optimization Online (2009)

2009

Cited alongside, same era.

E. G. Birgin, J. L. Gardenghi, J. M. Martínez, S. A. Santos, and Ph. L. Toint: Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models. Mathematical Programming 163

2017

Cited alongside, same era.

Grapiglia, G.N., Nesterov, Yu.: Regularized Newton Methods for minimizing functions with Hölder continuous Hessians. SIAM Journal on Optimization 27

2017

Cited alongside, same era.

Martínez, J.M.: On high-order model regularization for constrained optimization. SIAM Journal on Optimization 27

2017

Cited alongside, same era.

Nesterov, Yu: Lectures on Convex Optimization, 2nd Edition. Springer (2018)

2018

Cited alongside, same era.

Cartis, C., Gould, N.I.M., and Toint, Ph.L.: Universal regularized methods - varying the power, the smoothness, and the accuracy. SIAM Journal on Optimization 29

2019

Closest in time.

Chen, X., Toint, Ph.L., Wang, H.: Partially separable convexly-constrained optimization with non-Lipschitzian singularities and its complexity. SIAM Journal on Optimization 29

2019

Closest in time.

Grapiglia, G.N., Nesterov, Yu.: Accelerated Regularized Newton Methods for Minimizing Composite Convex Functions. SIAM Journal on Optimization 29

2019

Closest in time.

Grapiglia, G.N., Nesterov, Yu.: On Inexact Solution of Auxiliary Problems in Tensor Methods for Convex Optimization. Optimization Methods and Software 36

2021

Closest in time.

Nesterov, Yu.: Implementable tensor methods in unconstrained convex optimization. Mathematical Programming 186

2021