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 …

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 …

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 …

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 …

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 …

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

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 …

The popular BFGS quasi-Newton minimization algorithm under reasonable conditions
converges globally on smooth convex functions. This result was proved by Powell in a …

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 …