Over the last two decades, it has been observed that using the gradient vector as a search
direction in large-scale optimization may lead to efficient algorithms. The effectiveness relies …

The Barzilai and Borwein gradient method for the solution of large scale unconstrained
minimization problems is considered. This method requires few storage locations and very …

A new nonmonotone line search algorithm is proposed and analyzed. In our scheme, we
require that an average of the successive function values decreases, while the traditional …

The PATH solver is an implementation of a stabilized Newton method for the solution of the
Mixed Complementarity Problem. The stabilization scheme employs a path-generation …

A few months ago, while preparing a lecture to an audience that included engineers and
numerical analysts, I asked myself the question: from the point of view of a user of nonlinear …

We introduce some new path-following methods for the solution of the linear
complementarity problem. We call these methods noninterior continuation methods since, in …

The technique of nonmonotone line search has received many successful applications and
extensions in nonlinear optimization. This paper provides some basic analyses of the …

In this paper, by using derivative-free line search, we propose a quasi-Newton method for
smooth nonlinear equations. Under appropriate conditions, we show that the proposed …

Railway passenger transportation plays a fundamental role in Europe, particularly in view of
the growing number of trains offering valuable services such as high speed travel, high …

The purpose of this paper is to discuss the potential of nonmonotone techniques for
enforcing convergence of unconstrained minimization algorithms from starting points distant …