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Convex Analysis and Monotone Operator Theory in Hilbert Spaces pp 447–463Cite as

Sums of Monotone Operators

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

Abstract

The sum of two monotone operators is monotone. However, maximal monotonicity of the sum of two maximally monotone operators is not automatic and requires additional assumptions. In this chapter, we provide flexible sufficient conditions for maximality. Under additional assumptions, conclusions can be drawn about the range of the sum, which is important for deriving surjectivity results. We also consider the parallel sum of two set-valued operators.

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Kelowna, BC, Canada

    Heinz H. Bauschke

  2. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Patrick L. Combettes

Authors
  1. Heinz H. Bauschke
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  2. Patrick L. Combettes
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Bauschke, H.H., Combettes, P.L. (2017). Sums of Monotone Operators. In: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-48311-5_25

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