A perfect example for the BFGS method
YH Dai - Mathematical Programming, 2013 - Springer
Consider the BFGS quasi-Newton method applied to a general non-convex function that has
continuous second derivatives. This paper aims to construct a four-dimensional example …
continuous second derivatives. This paper aims to construct a four-dimensional example …
[HTML][HTML] The global convergence of a modified BFGS method for nonconvex functions
G Yuan, Z Sheng, B Wang, W Hu, C Li - Journal of Computational and …, 2018 - Elsevier
The standard BFGS method plays an important role among the quasi-Newton algorithms for
constrained/un-constrained optimization problems. However, Dai (2003) constructed a …
constrained/un-constrained optimization problems. However, Dai (2003) constructed a …
[HTML][HTML] Global convergence of BFGS and PRP methods under a modified weak Wolfe–Powell line search
G Yuan, Z Wei, X Lu - Applied Mathematical Modelling, 2017 - Elsevier
The BFGS method is one of the most effective quasi-Newton algorithms for optimization
problems. However, its global convergence for general functions is still open. In this paper …
problems. However, its global convergence for general functions is still open. In this paper …
On the global convergence of the BFGS method for nonconvex unconstrained optimization problems
DH Li, M Fukushima - SIAM Journal on Optimization, 2001 - SIAM
This paper is concerned with the open problem of whether the BFGS method with inexact
line search converges globally when applied to nonconvex unconstrained optimization …
line search converges globally when applied to nonconvex unconstrained optimization …
A modified BFGS algorithm for unconstrained optimization
Y Yuan - IMA Journal of Numerical Analysis, 1991 - academic.oup.com
In this paper we present a modified BFGS algorithm for unconstrained optimization. The
BFGS algorithm updates an approximate Hessian which satisfies the most recent quasi …
BFGS algorithm updates an approximate Hessian which satisfies the most recent quasi …
[HTML][HTML] A globally convergent BFGS method with nonmonotone line search for non-convex minimization
Y Xiao, H Sun, Z Wang - Journal of computational and applied mathematics, 2009 - Elsevier
In this paper, we propose a modified BFGS (Broyden–Fletcher–Goldfarb–Shanno) method
with nonmonotone line search for unconstrained optimization. Under some mild conditions …
with nonmonotone line search for unconstrained optimization. Under some mild conditions …
Global convergece of the bfgs algorithm with nonmonotone linesearch ∗this work is supported by national natural science foundation$ef:
G Liu, J Han, D Sun - Optimization, 1995 - Taylor & Francis
In this paper based on the nonmonotone linesearch technique of Grippo, et al ([4]) we
propose a class of nonmonotone linesearches which includes many linesearches used in …
propose a class of nonmonotone linesearches which includes many linesearches used in …
Convergence properties of the BFGS algoritm
YH Dai - SIAM Journal on Optimization, 2002 - SIAM
The BFGS method is one of the most famous quasi-Newton algorithms for unconstrained
optimization. In 1984, Powell presented an example of a function of two variables that shows …
optimization. In 1984, Powell presented an example of a function of two variables that shows …
Block BFGS methods
W Gao, D Goldfarb - SIAM Journal on Optimization, 2018 - SIAM
We introduce a quasi-Newton method with block updates called block BFGS. We show that
this method, performed with inexact Armijo--Wolfe line searches, converges globally and Q …
this method, performed with inexact Armijo--Wolfe line searches, converges globally and Q …