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Regularization Procedures for Monotone Operators: Recent Advances

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Book cover Fixed-Point Algorithms for Inverse Problems in Science and Engineering

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

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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.

AMS 2010 Subject Classification: 47H05, 46B10, 54C60, 26B25

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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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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Street, Block 8, 1113, Sofia, Bulgaria

    J. P. Revalski

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  1. J. P. Revalski
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Correspondence to J. P. Revalski .

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Editors and Affiliations

  1. Okanagan Campus, Department of Mathematics and Statistic, University of British Columbia, Kelowna, V1V 1V7, British Columbia, Canada

    Heinz H. Bauschke

  2. School of Mathematics & Statistics, Division of Information Technology, University of South Australia, Mawson Lakes Blvd., Mawson Lakes, 5095, South Australia, Australia

    Regina S. Burachik

  3. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Place Jussieu 4, Paris, 75005, France

    Patrick L. Combettes

  4. Dept. Physics, Lab. Atomic & Solid State, Cornell University, Clark Hall, Ithaca, 14853-2501, New York, USA

    Veit Elser

  5. Institut für Numerische und Angewandte M, Universität Göttingen, Lotzestr. 16-18, Göttingen, 37073, Germany

    D. Russell Luke

  6. Faculty of Mathematics, Dept. Combinatorics & Optimization, University of Waterloo, Waterloo, N2L 3G1, Ontario, Canada

    Henry Wolkowicz

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Revalski, J.P. (2011). Regularization Procedures for Monotone Operators: Recent Advances. In: Bauschke, H., Burachik, R., Combettes, P., Elser, V., Luke, D., Wolkowicz, H. (eds) Fixed-Point Algorithms for Inverse Problems in Science and Engineering. Springer Optimization and Its Applications(), vol 49. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9569-8_16

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