A Projected Inexact Levenberg-Marquardt Method for the Completely Positive Matrix Factorization
提出一种投影非精确莱文贝格-马夸特方法求解完全正矩阵分解问题，通过非精确方向降低计算成本，并证明全局收敛性，数值实验表明该方法与近端梯度或交替最小化方法相比具有竞争力。
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.