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We provide convergence rates for Krylov subspace solutions to the trust-region and cubic-regularized (nonconvex) quadratic problems.
Methods of conjugate gradients for solving linear systems
M. Hestenes and E. Stiefel · 1952
Earlier work this paper cites.
A block Lanczos algorithm for computing the q algebraically largest eigenvalues and a corresponding eigenspace of large, sparse, real symmetric matrices
J. Cullum and W. E. Donath · 1974
Earlier work this paper cites.
The block Lanczos method for computing eigenvalues
G. H. Golub and R. Underwood · 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.
Problem Complexity and Method Efficiency in Optimization
A. Nemirovski and D. Yudin · 1983
Earlier work this paper cites.
Matrix computations
G. Golub and C. V. Loan · 1989
Earlier work this paper cites.
Error bounds in the simple Lanczos procedure for computing functions of symmetric matrices and eigenvalues
V. Druskin and L. Knizhnerman · 1991
Earlier work this paper cites.
Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start
J. Kuczynski and H. Wozniakowski · 1992
Earlier work this paper cites.
Efficient methods in convex programming
A. Nemirovski · 1994
Earlier work this paper cites.
Fast exact multiplication by the Hessian
B. A. Pearlmutter · 1994
Earlier work this paper cites.
Numerical Linear Algebra
L. N. Trefethen and D. Bau III · 1997
Earlier work this paper cites.
Solving the trust-region subproblem using the Lanczos method
N. I. M. Gould, S. Lucidi, M. Roma, and P. L. Toint · 1999
Earlier work this paper cites.
Trust Region Methods
A. R. Conn, N. I. M. Gould, and P. L. Toint · 2000
Earlier work this paper cites.
Fast curvature matrix-vector products for second-order gradient descent
N. N. Schraudolph · 2002
Cited alongside, same era.
GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization
N. I. Gould, D. Orban, and P. L. Toint · 2003
Cited alongside, same era.
Introductory Lectures on Convex Optimization
Y. Nesterov · 2004
Cited alongside, same era.
Cubic regularization of Newton method and its global performance
Y. Nesterov and B. Polyak · 2006
Cited alongside, same era.
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J. Nocedal and S. J. Wright · 2006
Cited alongside, same era.
On accelerated proximal gradient methods for convex-concave optimization
P. Tseng · 2008
Cited alongside, same era.
Finding approximate local minima faster than gradient descent
N. Agarwal, Z. Allen-Zhu, B. Bullins, E. Hazan, and T. Ma · 2017
Later among the works it cites.
Linear coupling: An ultimate unification of gradient and mirror descent
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Later among the works it cites.
Stability of the Lanczos method for matrix function approximation
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Later among the works it cites.
Accelerated gradient descent escapes saddle points faster than gradient descent
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Later among the works it cites.
Sub-sampled cubic regularization for non-convex optimization
J. M. Kohler and A. Lucchi · 2017
Later among the works it cites.
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Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results
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A fast divide-and-conquer algorithm for computing the spectra of real symmetric tridiagonal matrices
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Convergence rate analysis of a stochastic trust region method for nonconvex optimization
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Gradient descent efficiently finds the cubic-regularized non-convex Newton step
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Fast black-box variational inference through stochastic trust-region optimization
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Stochastic cubic regularization for fast nonconvex optimization
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On the generalized Lanczos trust-region method
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Accelerated methods for non-convex optimization
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trlib: A vector-free implementation of the GLTR method for iterative solution of the trust region problem
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