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 …
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 …
Y Zhang, RP Tewarson - IMA Journal of Numerical Analysis, 1988 - academic.oup.com
Most popular quasi-Newton methods for unconstrained optimization are from the one- parameter Broyden's family, especially from a subset of the family: the so-called convex …
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 …
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 …
The classical convergence analysis of quasi-Newton methods assumes that function and gradient evaluations are exact. In this paper, we consider the case when there are …
G Yuan, M Zhang, Y Zhou - Applied Mathematics Letters, 2022 - Elsevier
Abstract The Broyden–Fletcher–Goldfarb–Shanno (BFGS) method plays an important role among the quasi-Newton algorithms for nonconvex and unconstrained optimization …
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 …
L Han, M Neumann - International Journal of Applied Mathematics, 2003 - researchgate.net
We propose a line search algorithm for unconstrained optimization in which the search direction is a combination of the quasi–Newton and the steepest descent directions. We …