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Maximal Monotone Inclusions and Fitzpatrick Functions
J.M. Borwein,
Published in Springer New York LLC
2016
Volume: 171
   
Issue: 3
Pages: 757 - 784
Abstract
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. © 2015, Springer Science+Business Media New York.
About the journal
JournalData powered by TypesetJournal of Optimization Theory and Applications
PublisherData powered by TypesetSpringer New York LLC
ISSN00223239