An incremental aggregated proximal ADMM for linearly constrained nonconvex optimization with application to sparse logistic regression problems

摘要

We propose an incremental aggregated proximal alternating direction method of multipliers (IAPADMM) for solving a class of nonconvex optimization problems with linear constraints. The new method inherits the advantages of the classical alternating direction method of multipliers and the incremental aggregated proximal method, which have been well studied for structured optimization problems. With some calm conditions, we prove that any limit point of the sequence generated by IAPADMM is the critical point of the considered problem. Furthermore, when the objective function satisfies the Kurdyka-tojasiewicz property, we obtain the global convergence of the proposed method. Moreover, some numerical results are reported to illustrate the effectiveness and advantage of the new method. (C) 2021 Elsevier B.V. All rights reserved.