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

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 …

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 …

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 …

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 …

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 …

Abstract The Broyden–Fletcher–Goldfarb–Shanno (BFGS) method plays an important role
among the quasi-Newton algorithms for nonconvex and unconstrained optimization …

In this paper, we propose a modified BFGS (Broyden–Fletcher–Goldfarb–Shanno) method
with nonmonotone line search for unconstrained optimization. Under some mild conditions …

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 …