On the contraction-proximal point algorithms with multi-parameters

摘要

In this paper we consider the contraction-proximal point algorithm: x_(n+1) = α_nu + λ_nx_n + γ_nJ_(βn)x_n, where J_(βn) denotes the resolvent of a monotone operator A. Under the assumption that lim_n α_n = 0, Σ_n α_n = ∞, lim inf_n β_n > 0, and lim inf_n γ_n > 0, we prove the strong convergence of the iterates as well as its inexact version. As a result we improve and recover some recent results by Boikanyo and Morosanu.