On the contraction-proximal point algorithms with multi-parameters

Fenghui Wang () and Huanhuan Cui

Journal of Global Optimization, 2012, vol. 54, issue 3, 485-491

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 α n = 0, ∑ 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. Copyright Springer Science+Business Media, LLC. 2012

Keywords: Maximal monotone operator; Proximal point algorithm; Firmly nonexpansive operator; 47J20; 49J40 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10898-011-9772-4

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