A Projected Inexact Levenberg-Marquardt Method for the Completely Positive Matrix Factorization

Abstract In this work we propose and analyze a projected Levenberg–Marquardt method for solving completely positive matrix factorization problems. Instead of computing the exact Levenberg–Marquardt direction, we introduce an inexact direction which simplifies the calculations and reduces the computational cost. Global convergence results are established for the proposed method endowed with a non-monotone line search. A series of numerical experiments on different classes of the problem are carried out and indicate that the new Projected Inexact Levenberg–Marquardt algorithm is competitive with well-established alternatives such as algorithms based on proximal gradient or alternating minimization methods.