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

In this paper, by using a so-called fixed steplength strategy, we propose a BFGS method
without use of line searches for unconstrained optimization. Under mild conditions, we show …

In this paper, we consider an unconstrained optimization problem and propose a new family
of modified BFGS methods to solve it. As it is known, classic BFGS method is not always …

In this paper, we propose a modification of the BFGS method for unconstrained optimization.
A remarkable feature of the proposed method is that it possesses a global convergence …

In this paper, a new nonmonotone BFGS algorithmfor unconstrained optimization is
introduced. Under mild conditions, the global convergence of this new algorithm on convex …

In this paper, we propose a new nonmonotone Armijo type line search and prove that the
MBFGS method proposed by Li and Fukushima with this new line search converges globally …

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 …

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, a new inexact line search rule is presented, which is a modified version of the
classical Armijo line search rule. With lower cost of computation, a larger descent magnitude …

Using chain rule, we propose a modified secant equation to get a more accurate
approximation of the second curvature of the objective function. Then, based on this …