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Another version of the proximal point algorithm in a Banach space. (English) Zbl 1167.49031
Summary: 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 are also presented in this paper.

MSC:
49N15 Duality theory (optimization)
49M15 Newton-type methods
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