In this paper we study a broad class of nonconvex and nonsmooth minimization problems, whose objective function is the sum of a smooth function of the entire variables and two nonsmooth functions of each variable. We adopt the framework of the proximal alternating linearized minimization (PALM), together with the inertial strategy to accelerate the convergence. Since the inertial step is performed once the x-subproblem/y-subproblem is updated, the algorithm is a Gauss–Seidel type inertial proximal alternating linearized minimization (GiPALM) algorithm. Under the assumption that the underlying functions satisfy the Kurdyka–Łojasiewicz (KL) property and some suitable conditions on the parameters, we prove that each bounded sequence generated by GiPALM globally converges to a critical point. We apply the algorithm to signal recovery, image denoising and nonnegative matrix factorization models, and compare it with PALM and the inertial proximal alternating linearized minimization.

在本文中，我们研究了一大类非凸和非光滑最小化问题，其目标函数是整个变量的光滑函数和每个变量的两个非光滑函数的和。我们采用近端交替线性化最小化（PALM）的框架以及惯性策略来加速收敛。由于惯性步骤执行一次，x-子问题/ y-subproblem已更新，该算法是高斯-塞德尔式惯性近端交替线性最小化（GiPALM）算法。假设基础函数满足Kurdyka–Łojasiewicz（KL）性质，并在参数上满足一些合适的条件，我们证明GiPALM生成的每个有界序列都全局收敛到一个临界点。我们将该算法应用于信号恢复，图像去噪和非负矩阵分解模型，并将其与PALM和惯性近端交替线性化最小化进行比较。