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 …

The standard BFGS method plays an important role among the quasi-Newton algorithms for
constrained/un-constrained optimization problems. However, Dai (2003) constructed a …

A simple three-term conjugate gradient algorithm which satisfies both the descent condition
and the conjugacy condition is presented. This algorithm is a modification of the Hestenes …

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 …

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 …

Another hybrid conjugate gradient algorithm is subject to analysis. The parameter β k is
computed as a convex combination of β^ HS _ k (Hestenes-Stiefel) and β^ DY _ k (Dai …

Although quasi-Newton algorithms generally converge in fewer iterations than conjugate
gradient algorithms, they have the disadvantage of requiring substantially more storage. An …

This paper analyzes algorithms from the Broyden class of quasi-Newton methods for
nonlinear unconstrained optimization. This class depends on a parameter \phi_k, for which …

Based upon analysis and numerical experience, the BFGS (Broyden–Fletcher–Goldfarb–
Shanno) algorithm is currently considered to be one of the most effective algorithms for …

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 …