Barzilai and Borwein conjugate gradient method equipped with a non-monotone line search technique and its application on non-negative matrix factorization
This is an incremental improvement for optimization practitioners, offering a modified method with proven convergence for specific applications like non-negative matrix factorization.
The authors tackled unconstrained nonlinear optimization by proposing a new non-monotone conjugate gradient method with a trigonometric function for parameter calculation and a Barzilai-Borwein step size, achieving global convergence and testing it on standard problems and non-negative matrix factorization.
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.