A proximal point algorithm converging strongly for general errors

Journal article

Authors/Editors

Oganeditse, Boikanyo

Research Areas

ENGINEERING AND TECHNOLOGY (Frascati classification)

Publication Details

Subtitle: A proximal point algorithm converging strongly for general errors

Publisher: Springer Verlag (Germany)

Publication year: 2010

Journal: Optimization Letters (1862-4472)

Volume number: 4

Issue number: 4

Start page: 635

End page: 641

Number of pages: 7

ISSN: 1862-4472

eISSN: 1862-4480

URL: https://link.springer.com/article/10.1007/s11590-010-0176-z

Languages: English-United States (EN-US)

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Abstract

In this paper a proximal point algorithm (PPA) for maximal monotone operators with appropriate regularization parameters is considered. A strong convergence result for PPA is stated and proved under the general condition that the error sequence tends to zero in norm. Note that Rockafellar (SIAM J Control Optim 14:877-898, 1976) assumed summability for the error sequence to derive weak convergence of PPA in its initial form, and this restrictive condition on errors has been extensively used so far for different versions of PPA. Thus this Note provides a solution to a long standing open problem and in particular offers new possibilities towards the approximation of the minimum points of convex functionals.

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