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Another version of the proximal point algorithm in a Banach space

✍ Scribed by Ya.I. Alber; Jen-Chih Yao

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 660 KB
Volume: 70
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2008.04.019

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✦ Synopsis

In this paper, we study some non-traditional schemes of proximal point algorithm for nonsmooth convex functionals in a Banach space. The proximal approximations to their minimal points and/or their minimal values are considered separately for unconstrained and constrained minimization problems on convex closed sets. For the latter we use proximal point algorithms with the metric projection operators and first establish the estimates of the convergence rate with respect to functionals. We also investigate the perturbed projection proximal point algorithms and prove their stability. Some results concerning the classical proximal point method for minimization problems in a Banach space is also presented in this paper.

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