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 seminal paper by Barzilai and Borwein (1988) has given rise to an extensive
investigation, leading to the development of effective gradient methods. Several steplength …

We propose a family of spectral gradient methods, whose stepsize is determined by a
convex combination of the long Barzilai–Borwein (BB) stepsize and the short BB stepsize …

We propose a new gradient method for quadratic programming, named SDC, which
alternates some steepest descent (SD) iterates with some gradient iterates that use a …

The aim of this paper is to deepen the convergence analysis of the scaled gradient
projection (SGP) method, proposed by Bonettini et al in a recent paper for constrained …

Gradient projection methods represent effective tools for solving large-scale constrained
optimization problems thanks to their simple implementation and low computational cost per …

The primary aim of this paper is to provide a review of the last few decades of research
focused on delayed gradient methods for solving symmetric positive definite linear systems …

Abstract The Barzilai and Borwein gradient method has received a significant amount of
attention in different fields of optimization. This is due to its simplicity, computational …

In this paper, we introduce a new concept of approximate optimal stepsize for gradient
method, use it to interpret the Barzilai-Borwein (BB) method, and present an efficient …

The role of the steplength selection strategies in gradient methods has been widely
investigated in the last decades. Starting from the work of Barzilai and Borwein (1988), many …