Efficient hybrid algorithm for nonnegative matrix factorization based on modified nonmonotone linear search

In this paper, we present a modified nonmonotone line search algorithm that employs a variable parameter to control the degree of nonmonotonicity. This modification enhances both the probability of identifying the global minimum and the rate of convergence. Within the framework of alternating nonnegative least squares (ANLS), we propose a hybrid algorithm that employs either the modified nonmonotone projected Barzilai-Borwein method and the block coordinate descent method to address the subproblems in each iteration. To further accelerate convergence, we integrate a technique that allows for a larger step size. Under mild assumptions, we establish the global convergence of the algorithm. Numerical experiments conducted on both synthetic and real datasets demonstrate that the proposed algorithm is efficient for nonnegative matrix factorization (NMF) and outperforms other state-of-the-art methods.