Accelerated derivative-free spectral residual method for nonlinear systems of equations

TL;DR

This paper introduces an accelerated spectral residual method implemented in R for solving nonlinear systems, demonstrating improved robustness and efficiency through numerical experiments against standard solvers and non-accelerated versions.

Contribution

It presents an R implementation of an accelerated spectral residual method using the Sequential Secant acceleration, enhancing robustness and efficiency over existing methods.

Findings

The accelerated method outperforms the non-accelerated version in robustness.

The method compares favorably with NITSOL in numerical experiments.

An interface between R and the CUTEst collection is provided.

Abstract

Spectral residual methods are powerful tools for solving nonlinear systems of equations without derivatives. In a recent paper, it was shown that an acceleration technique based on the Sequential Secant Method can greatly improve its efficiency and robustness. In the present work, an R implementation of the method is presented. Numerical experiments with a widely used test bed compares the presented approach with its plain (i.e. non-accelerated) version that makes part of the R package BB. Additional numerical experiments compare the proposed method with NITSOL, a state-of-the-art solver for nonlinear systems. The comparison shows that the acceleration process greatly improves the robustness of its counterpart included in the existent R package. As a by-product, an interface is provided between R and the consolidated CUTEst collection, which contains over a thousand nonlinear programming problems of all types and represents a standard for evaluating the performance of optimization methods.