Global optimization through a stochastic perturbation of the Polak–Ribière conjugate gradient method

Abstract

We develop a new modified Polak–Ribière conjugate gradient method by considering a random perturbation. Our approach is suitable for solving a large class of optimization problems on a rectangle of Rn or unconstrained problems. Theoretical results ensure that the proposed method converges to a global minimizer. Numerical experiments are achieved on some typical test problems, particularly the engineering problem of Lennard-Jones clusters. A comparison with well known methods is carried out to show the performance of our algorithm.