On the contraction-proximal point algorithms with multi-parameters

Authors:
Fenghui Wang;Huanhuan Cui
Affiliations:
Department of Mathematics, Luoyang Normal University, Luoyang, China 471022;Department of Mathematics, Luoyang Normal University, Luoyang, China 471022
Venue:
Journal of Global Optimization
Year:
2012

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Abstract

In this paper we consider the contraction-proximal point algorithm: $${x_{n+1}=\alpha_nu+\lambda_nx_n+\gamma_nJ_{\beta_n}x_n,}$$ where $${J_{\beta_n}}$$ denotes the resolvent of a monotone operator A. Under the assumption that lim n 驴 n = 0, 驴 n 驴 n = 驴, lim inf n β n 0, and lim inf n 驴 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.