Monotonically accelerated proximal gradient for nonnegative tensor decomposition

Efficient tensor decomposition requires stable and convergent optimization algorithms. The accelerated proximal gradient (APG) is a workhorse algorithm for nonnegative tensor decomposition. For large-scale tensors, APG is always implemented to optimize the subproblems in the block coordinate descent framework. However, APG cannot guarantee monotonic convergence in the optimization process. In this paper, we develop monotonically accelerated algorithms to improve the efficiency of tensor decomposition. We propose four criteria to monitor the convergence state in the subproblem. Based on each criterion, we propose monotonic convergence rules for the subproblem. We evaluate the monotonically accelerated algorithms via six experiments covering a wide range of types of tensors. The experimental results demonstrate that our proposed algorithms with monotonic convergence monitoring have significant acceleration effects and high precision compared with those without monitoring. After the experiments, we present the selection rule of the monotonic monitoring criterion for different types of tensors.