Modified Proximal-Point Algorithm for Maximal Monotone Operators in Banach Spaces

L. Li and W. Song ()
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L. Li: Northeast Normal University
W. Song: Harbin Normal University

Journal of Optimization Theory and Applications, 2008, vol. 138, issue 1, No 4, 45-64

Abstract: Abstract We introduce an iterative sequence for finding the solution to 0∈T(v), where T : E⇉E * is a maximal monotone operator in a smooth and uniformly convex Banach space E. This iterative procedure is a combination of iterative algorithms proposed by Kohsaka and Takahashi (Abstr. Appl. Anal. 3:239–249, 2004) and Kamamura, Kohsaka and Takahashi (Set-Valued Anal. 12:417–429, 2004). We prove a strong convergence theorem and a weak convergence theorem under different conditions respectively and give an estimate of the convergence rate of the algorithm. An application to minimization problems is given.

Keywords: Proximal-point algorithms; Uniformly convex and smooth Banach spaces; Maximal monotone operators; Strong and weak convergence (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-008-9370-x

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