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

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.