Barzilai and Borwein conjugate gradient method equipped with a non-monotone line search technique and its application on non-negative matrix factorization

TL;DR

This paper introduces a novel non-monotone conjugate gradient method with a trigonometric-based line search and Barzilai-Borwein step size, demonstrating improved convergence and efficiency on optimization and non-negative matrix factorization problems.

Contribution

It presents a new non-monotone conjugate gradient algorithm with a trigonometric line search and Barzilai-Borwein step size, proving global convergence.

Findings

Proven global convergence under certain conditions.

Enhanced efficiency demonstrated on test problems.

Effective application to non-negative matrix factorization.

Abstract

In this paper, we propose a new non-monotone conjugate gradient method for solving unconstrained nonlinear optimization problems. We first modify the non-monotone line search method by introducing a new trigonometric function to calculate the non-monotone parameter, which plays an essential role in the algorithm's efficiency. Then, we apply a convex combination of the Barzilai-Borwein method for calculating the value of step size in each iteration. Under some suitable assumptions, we prove that the new algorithm has the global convergence property. The efficiency and effectiveness of the proposed method are determined in practice by applying the algorithm to some standard test problems and non-negative matrix factorization problems.