What question did this study set out to answer?

The aim is to enhance the performance of the PRP conjugate gradient algorithm in large-scale optimization.

January 18, 2026

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

Key Points

The aim is to enhance the performance of the PRP conjugate gradient algorithm in large-scale optimization.
Modified the PRP algorithm using an optimal parameter choice based on Barzilai-Borwein.
Conducted numerical experiments on standard optimization benchmarks.
Applied the algorithm to image restoration tasks.
The proposed method showed improved convergence efficiency compared to established algorithms.
It achieved better solution quality across various tests.

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.

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

Key Points

Abstract

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