A supplement to a regularization method for the proximal point algorithm

Satit Saejung ()

Journal of Global Optimization, 2013, vol. 56, issue 1, 129 pages

Abstract: The purpose of this paper is to show that the iterative scheme recently studied by Xu (J Glob Optim 36(1):115–125, 2006 ) is the same as the one studied by Kamimura and Takahashi (J Approx Theory 106(2):226–240, 2000 ) and to give a supplement to these results. With the new technique proposed by Maingé (Comput Math Appl 59(1):74–79, 2010 ), we show that the convergence of the iterative scheme is established under another assumption. It is noted that if the computation error is zero or the approximate computation is exact, our new result is a genuine generalization of Xu’s result and Kamimura–Takahashi’s result. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Maximal monotone operator; Proximal point algorithm; Hilbert space (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-9931-2

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