Fetching the paper…
Reading the bibliography…
We propose a new family of multilevel methods for unconstrained minimization.
A multi-level adaptative solution to boundary-value problems
A. Brandt · 1977
Earlier work this paper cites.
The modification of Newton’s method for unconstrained optimization by bounding cubic terms
A. Griewank · 1981
Earlier work this paper cites.
Multi-grid methods and applications
W. Hackbusch · 1985
Earlier work this paper cites.
Tensor methods for large, sparse unconstrained optimization
A. Bouaricha · 1997
Earlier work this paper cites.
A Multigrid Tutorial
W. Briggs, V. Henson, and S. McCormick · 2000
Earlier work this paper cites.
Trust region methods
A. R. Conn, N. Gould, and Ph. L. Toint · 2000
Earlier work this paper cites.
A multigrid approach to discretized optimization problems
S.G. Nash · 2000
Earlier work this paper cites.
Model problems for the multigrid optimization of systems governed by differential equations
R.M. Lewis and S.G. Nash · 2005
Earlier work this paper cites.
Cubic regularization of Newton method and its global performance
Y. Nesterov and B.T. Polyak · 2006
Earlier work this paper cites.
Numerical Optimization
J. Nocedal and S. Wright · 2006
Cited alongside, same era.
Recursive trust-region methods for multiscale nonlinear optimization
S. Gratton, A. Sartenaer, and Ph L. Toint · 2008
Cited alongside, same era.
A line search multigrid method for large-scale nonlinear optimization
Z. Wen and D. Goldfarb · 2009
Cited alongside, same era.
On the complexity of steepest descent, Newton’s and regularized Newton’s methods for nonconvex unconstrained optimization problems
C. Cartis, N.I.M. Gould, and P. L. Toint · 2010
Cited alongside, same era.
Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics
A. Brandt and O. E. Livne · 2011
Cited alongside, same era.
Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results
Properties of a class of multilevel optimization algorithms for equality constrained problems
S.G. Nash · 2014
Later among the works it cites.
Recent advances in trust region algorithms
Y. Yuan · 2015
Later among the works it cites.
A first-order multigrid method for bound-constrained convex optimization
M. Kočvara and S. Mohammed · 2016
Later among the works it cites.
Julia: A fresh approach to numerical computing
J. Bezanson, A. Edelman, S. Karpinski, and V. Shah · 2017
Later among the works it cites.
Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
E. G. Birgin, J. L. Gardenghi, J. M. Martínez, S. A. Santos, and Ph. L. Toint · 2017
Later among the works it cites.
A tensor trust-region model for nonlinear system
S. Wang and S. Liu · 2018
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
C. Cartis, N. Gould, and P. L. Toint · 2011
Cited alongside, same era.
Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity
C. Cartis, N.I.M. Gould, and P. L. Toint · 2011
Cited alongside, same era.
Using inexact gradients in a multilevel optimization algorithm
R.M. Lewis and S.G. Nash · 2013
Cited alongside, same era.
Nonlinear stepsize control, trust regions and regularizations for unconstrained optimization
P. L. Toint · 2013
Cited alongside, same era.
Later among the works it cites.
On the quadratic convergence of the cubic regularization method under a local error bound condition
M.C. Yue, Z. Zhou, and A.M.C. So · 2018
Later among the works it cites.
On the approximation of the solution of partial differential equations by artificial neural networks trained by a multilevel Levenberg-Marquardt method
H. Calandra, S. Gratton, E. Riccietti, and X. Vasseur · 2019
Closest in time.
Complexity of partially separable convexly constrained optimization with non-lipschitzian singularities
X. Chen, P. Toint, and H. Wang · 2019
Closest in time.