The conjugate gradient methods (CGMs) are very effective iterative methods for solving
large-scale unconstrained optimization. The aim of this work is to improve the Fletcher …

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 …

In view of a direct and simple improvement of vanilla SGD, this paper presents a fine-tuning
of its step-sizes in the mini-batch case. For doing so, one estimates curvature, based on a …

The spectral conjugate gradient methods are very interesting and have been proved to be
effective for strictly convex quadratic minimisation. In this paper, a new spectral conjugate …

In this paper we introduce a new concept of approximate optimal stepsize for gradient
method, use it to interpret the nice numerical effect of the Barzilai–Borwein (BB) method, and …

This paper presents a new method for steplength selection in the frame of spectral gradient
methods. The steplength formula is based on the interpolation scheme as well as some …

In this paper, we present two choices of structured spectral gradient methods for solving
nonlinear least squares problems. In the proposed methods, the scalar multiple of identity …

Based on two modified secant equations proposed by Yuan, and Li and Fukushima, we
extend the approach proposed by Andrei, and introduce two hybrid conjugate gradient …

Conjugate gradient methods have played a special role for solving large scale optimization
problems due to the simplicity of their iteration, convergence properties and their low …

In this paper, a derivative-free Barzilai-Borweinlike algorithm is developed for solving large-
scale non-linear systems of equations. The algorithm is based on approximating the …