Maximal monotone inclusions and Fitzpatrick functions

Title: Maximal monotone inclusions and Fitzpatrick functions
Creator: Borwein, J. M.; Dutta, J.
Relation: Journal of Optimization Theory and Applications Vol. 171, Issue 3, p. 757-784
Publisher Link: http://dx.doi.org/10.1007/s10957-015-0813-x
Publisher: Springer
Resource Type: journal article
Date: 2016
Description: In this paper, we study maximal monotone inclusions from the perspective of gap functions. We propose a very natural gap function for an arbitrary maximal monotone inclusion and will demonstrate how naturally this gap function arises from the Fitzpatrick function, which is a convex function, used to represent maximal monotone operators. This allows us to use the powerful strong Fitzpatrick inequality to analyse solutions of the inclusion. We also study the special cases of a variational inequality and of a generalized variational inequality problem. The associated notion of a scalar gap is also considered in some detail. Corresponding local and global error bounds are also developed for the maximal monotone inclusion.
Subject: maximal monotone operator; monotone inclusions; variational inequality; Fitzpatrick function; gap functions; error bounds
Identifier: http://hdl.handle.net/1959.13/1338273
Identifier: uon:27998
Identifier: ISSN:0022-3239
Language: eng
Reviewed

		Thumbnail	File	Description	Size	Format