Proximal point methods revisited

Journal article

Authors / Editors

Oganeditse, Boikanyo

Research Areas

ENGINEERING AND TECHNOLOGY (Frascati classification)

Publication Details

Subtitle: Proximal point methods revisited

Publisher: SAGE Publications (UK and US)

Publication year: 2011

Journal: Journal of Mixed Methods Research (1558-6898)

Volume number: 1389

Issue number: 1

Start page: 893

End page: 896

Number of pages: 4

ISSN: 1558-6898

eISSN: 1558-6901

URL: https://aip.scitation.org

Languages: English-United States (EN-US)

View on publisher site

Abstract

The proximal point methods have been widely used in the last decades to approximate the solutions of nonlinear equations associated with monotone operators. Inspired by the iterative procedure defined by B. Martinet (1970), R.T. Rockafellar introduced in 1976 the so-called proximal point algorithm (PPA) for a general maximal monotone operator. The sequence generated by this iterative method is weakly convergent under appropriate conditions, but not necessarily strongly convergent, as proved by O. Güler (1991). This fact explains the introduction of different modified versions of the PPA which generate strongly convergent sequences under appropriate conditions, including the contraction-PPA defined by H.K. Xu in 2002. Here we discuss Xu's modified PPA as well as some of its generalizations. Special attention is paid to the computational errors, in particular the original Rockafellar summability assumption is replaced by the condition that the error sequence converges to zero strongly.

Keywords

No matching items found.

Documents