In this paper we present a modified BFGS algorithm for unconstrained optimization. The
BFGS algorithm updates an approximate Hessian which satisfies the most recent quasi …

Many methods for solving minimization problems are variants of Newton method, which
requires the specification of the Hessian matrix of second derivatives. Quasi-Newton …

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 …

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

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 …

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 …

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 method is the most effective of the quasi-Newton methods for solving
unconstrained optimization problems. Wei, Li, and Qi [16] have proposed some modified …

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 …