A modified BFGS method and its global convergence in nonconvex minimization

By Donghui Li, Masao Fukushima. 2001

425 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/88f463908b6be50d9ea69a833698fdd300bf2286

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. Albert S. Berahas
2. Peter Richtárik
3. Majid Jahani
4. Martin Takác
5. Aryan Mokhtari
6. Alejandro Ribeiro
7. Jie Liu
8. Nicolas Loizou

In Computational Theory and Mathematics

1. Albert S. Berahas
2. Alejandro Ribeiro
3. Martin Takác
4. Junzhou Huang
5. Zhepei Wang
6. Huan Zhu
7. Jie Liu
8. Fei Gao

In Numerical Analysis

1. Majid Jahani
2. Martin Takác
3. Alejandro Ribeiro
4. Aryan Mokhtari
5. Albert S. Berahas
6. Junzhou Huang
7. Zhepei Wang
8. Huan Zhu

Citations in the corpus

• Geometrically Constrained Trajectory Optimization for Multicopters (2021, methodology): “After obtaining all the gradients, the relaxation (98) is then efficiently solved by the Limitedmemory Broyden–Fletcher–Goldfarb–Shanno algorithm (LBFGS) (Liu and Nocedal 1989) with a modified updating rule (Li and Fukushima 2001) to ensure stability of the nonconvex minimization.”
• Global convergence of online limited memory BFGS (2014, background): “(68) To simplify the right hand side of (68) we should first know that for any vectors u1, u2, u3 and u4, we can write det(I + u1u T 2 + u3u T 4 ) = (1 + u T 1 u2)(1 + u T 3 u4) − (u T 1 u4)(u T 2 u3) – see, e.g., Li and Fukushima (2001), Lemma 3.3).”
• A Modified Hestenes-Stiefel-Type Derivative-Free Method for Large-Scale Nonlinear Monotone Equations (2020, methodology): “Based on the modified secant equation [10], Dai and Wen [47] propose a modified HS conjugate gradient method that can generate sufficient descent directions (i.”
• On the Acceleration of L-BFGS with Second-Order Information and Stochastic Batches (2018, positive): “As a well-suited approach to our algorithm, we employ a cautious strategy [16]: we skip the update, i.e., set is violated, where (cid:15) > 0 is a predefined positive constant.”
• When Relaxations Go Bad: "Differentially-Private" Machine Learning (2019, neutral): “While many first order [14, 37, 58, 78] and second order [40, 43] meth-ods exist to solve this minimization problem, the most basic procedure is gradient descent where we iteratively calculate the gradient of J ( θ ) with respect to θ and update θ with the gradient information.”
• Quasi-Newton Methods for Deep Learning: Forget the Past, Just Sample (2019, methodology): “To establish convergence in the nonconvex setting several techniques have been proposed [34, 35, 47].”