Regularization Procedures for Monotone Operators: Recent Advances

Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 49)

Abstract

In this, essentially survey, article we present some recent advances concerning two regularization procedures for monotone operators: extended and variational sums of maximal monotone operators and, the related to them, extended and variational compositions of monotone operators with linear continuous mappings.

Keywords

Maximal monotone operators Sums Compositions ​Graph-convergence Variational sum Extended sum Variational composition Yosida regularization Subdifferential 

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Notes

Acknowledgements

The author would like to thank Radu Boţ, Yboon García, Marc Lassonde and Constantin Zălinescu, whose valuable remarks after a careful reading of an earlier version of the manuscript, helped to present a more complete picture concerning the notions and the results in this article. The author is also grateful to two anonymous referees for their detailed remarks.

This article was prepared while the author was professeur associé in the group LAMIA in the Department of Mathematics and Informatics of the Université des Antilles et de la Guyane, Guadeloupe, France.

The author has been partially supported by the Bulgarian National Fund for Scientific Research, under grant DO02-360/2008.

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria

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