An Optimal Choice for Polak‐Ribière‐Polyak Conjugate Gradient Algorithm Based on Barzilai‐Borwein Approach for Large‐Scale Optimization Problems with Application

Numerical Linear Algebra with Applications 2026

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Authors: Jamilu Sabi'u, Ibrahim Mohammed Sulaiman, Aliyu Muhammed Awwal, Elissa Nadia Madi, Eihab B. M. Bashier
DOI: 10.1002/nla.70051
Cited by: 0
References: 22

Abstract

ABSTRACT This paper introduces a modified Polak‐Ribière‐Polyak Nonlinear (PRP) conjugate gradient algorithm, incorporating an optimal choice for the PRP parameter, guided by the Barzilai‐Borwein strategy, to enhance convergence behavior. This optimal parameter choice strengthens the algorithm's global convergence properties under mild assumptions on the objective function. Comprehensive numerical experiments on standard optimization benchmarks and image restoration tasks demonstrate that the proposed method consistently outperforms several established algorithms in both convergence efficiency and solution quality.

Fields of Study & Subjects

Advanced Optimization Algorithms Research Matrix Theory and Algorithms Optimization and Variational Analysis

Publication details

Journal / source
Numerical Linear Algebra with Applications
Volume
33
Issue
1
Publication date
15 January 2026
Language
EN