Convergence Properties of the BFGS Algoritm

By Yuhong Dai. SIAM Journal on Optimization, 2002

317 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5dfbfe0f4f6ca1372ddb97536023b17e8d464ed6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Peter Richtárik
2. Martin Takác
3. Nicolas Loizou
4. Albert S. Berahas
5. Majid Jahani
6. A. S. Lewis
7. Michael L. Overton
8. Jakub Konecný

In Computational Theory and Mathematics

1. A. S. Lewis
2. Michael L. Overton
3. Albert S. Berahas
4. Martin Takác
5. Majid Jahani
6. Peter Richtárik
7. Nicolas Loizou
8. Jakub Konecný

In Numerical Analysis

1. Michael L. Overton
2. A. S. Lewis
3. Martin Takác
4. Majid Jahani
5. Albert S. Berahas
6. Peter Richtárik
7. Daniel Petersson
8. Jakub Konecný

Citations in the corpus

• Nonsmooth optimization via quasi-Newton methods (2012, background): “If the convexity assumption is dropped, pathological counterexamples to convergence are known to exist [10,36], but it is widely accepted that the method works well in practice in the smooth, nonconvex case [29].”
• On the Acceleration of L-BFGS with Second-Order Information and Stochastic Batches (2018, unknown): “The standard BFGS updates can fail in handling non-convexity because of difficulty in approximating Hessian with a positive definite matrix [6, 21].”
• Quasi-Newton Methods for Deep Learning: Forget the Past, Just Sample (2019, background): “Nonconvex Functions For nonconvex functions, it is known that the (L)BFGS method can fail [16, 40].”