Difference-of-Convex Algorithm with Extrapolation for Nonconvex, Nonsmooth Optimization Problems
针对非凸可微函数与凸差函数之和的优化问题，提出一种结合Nesterov加速与凸差算法的新算法，证明其收敛性并在非负矩阵补全实验中优于已知方法。
In this paper, we focus on the problem of minimizing the sum of a nonconvex differentiable function and a difference of convex (DC) function, where the differentiable function is not restricted to the global Lipschitz gradient continuity assumption. This problem covers a broad range of applications in machine learning and statistics, such as compressed sensing, signal recovery, sparse dictionary learning, matrix factorization, etc. We first take inspiration from the Nesterov acceleration technique and the DC algorithm to develop a novel algorithm for the considered problem. We then study the subsequential convergence of our algorithm to a critical point. Furthermore, we justify the global convergence of the whole sequence generated by our algorithm to a critical point and establish its convergence rate under the Kurdyka–Łojasiewicz condition. Numerical experiments on the nonnegative matrix completion problem are performed to demonstrate the efficiency of our algorithm and its superiority over well-known methods.