A Modified Dai-Liao Spectral Conjugate Gradient Method with an Application to Signal Processing

TL;DR

This paper introduces a modified spectral conjugate gradient method with a new secant condition, ensuring global convergence and improved performance, demonstrated through numerical experiments and an application in signal processing.

Contribution

It presents a novel variant of the Dai-Liao spectral conjugate gradient method with a new secant condition and quasi-Newton directions, enhancing convergence and efficiency without line search.

Findings

Better convergence speed than existing methods

Higher computational efficiency in experiments

Effective application to signal processing tasks

Abstract

We propose and study a variant of the Dai-Liao spectral conjugate gradient method, developed through an analysis of eigenvalues and inspired by a modified secant condition. We show that our proposed method is globally convergent for general nonlinear functions under standard assumptions. By incorporating the new secant condition and a quasi-Newton direction, we introduce updated spectral parameters. These changes ensure that the resulting search direction satisfies the sufficient descent property without relying on any line search. Numerical experiments show that the proposed algorithm performs better than several existing methods in terms of convergence speed and computational efficiency. Its effectiveness is further demonstrated through an application to signal processing.