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 …

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 …

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

abstract In this paper we state some nonmonotone line search strategies for unconstrained
optimization algorithms. Abstracting from the concrete line search strategy we prove two …

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 …

We study the global convergence properties of the restricted Broyden class of quasi-Newton
methods, when applied to a convex objective function. We assume that the line search …

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 …

We study the self-scaling BFGS method of Oren and Luenberger (1974) for solving
unconstrained optimization problems. For general convex functions, we prove that the …

The BFGS update formula is shown to have an important property that is independent of the
algorithmic context of the update, and that is relevant to both constrained and unconstrained …