A fast computational Gauss–Seidel type iPALM algorithm using an incremental aggregated gradient strategy for weakly convex composite optimization problems with application in image processing - Jia, Zehui; Hou, Junru; Dong, Ping; Liu, Zhiyu (Journal of computational and applied mathematics, 2026)
In this paper, we propose a Gauss–Seidel type inertial proximal alternating linearized minimization method with incremental aggregated gradient (IAG-GiPALM) for solving a class of nonconvex and nonsmooth composite optimization problems, whose objective function is the sum of a finite number of smooth nonconvex functions and nonsmooth weakly convex functions. This new algorithm inherits the advantages of the Gauss–Seidel type inertial proximal alternating linearized minimization method (GiPALM) and the incremental aggregated proximal method. Under some mild conditions, we prove that any limit point of the sequence generated by IAG-GiPALM is a critical point of the optimization problems. Moreover, we establish the global convergence and convergence rate of the algorithm under the Kurdyka-Łojasiewicz property. In addition, some numerical results are conducted to demonstrate the efficiency of the new method.