On Extensions of Limited Memory Steepest Descent Method

TL;DR

This paper introduces extensions to the limited memory steepest descent method by combining spectral, cyclic, sweep, and delayed strategies, resulting in improved performance demonstrated through numerical experiments.

Contribution

It presents novel extensions to the limited memory steepest descent method, enhancing efficiency by integrating spectral and cyclic iteration strategies.

Findings

New methods outperform original versions in numerical tests

Extensions improve convergence speed and stability

Parallel implementation remarks provided

Abstract

We present some extensions to the limited memory steepest descent method based on spectral properties and cyclic iterations. Our aim is to show that it is possible to combine sweep and delayed strategies for improving the performance of gradient methods. Numerical results are reported which indicate that our new methods are better than the original version. Some remarks on the stability and parallel implementation are shown in the end.