Infimal Convolution

Bauschke, Heinz H.; Combettes, Patrick L.

doi:10.1007/978-1-4419-9467-7_12

Heinz H. Bauschke³ &
Patrick L. Combettes⁴

Part of the book series: CMS Books in Mathematics ((CMSBM))

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Abstract

This chapter is devoted to a fundamental convexity-preserving operation for functions: the infimal convolution. Its properties are investigated, with special emphasis on the Moreau envelope, which is obtained by convolving a function with the halved squared norm.

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Authors and Affiliations

Mathematics Irving K. Barber School, University of British Columbia, Kelowna, B.C., V1V 1V7, Canada
Heinz H. Bauschke
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie - Paris 6, 4, Place Jussieu, 75005, Paris, France
Patrick L. Combettes

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Heinz H. Bauschke
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Patrick L. Combettes
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Correspondence to Heinz H. Bauschke .

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Bauschke, H.H., Combettes, P.L. (2011). Infimal Convolution. In: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9467-7_12

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DOI: https://doi.org/10.1007/978-1-4419-9467-7_12
Published: 03 April 2011
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-9466-0
Online ISBN: 978-1-4419-9467-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

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