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Sums of Monotone Operators

  • Heinz H. Bauschke
  • Patrick L. Combettes
Chapter
  • 2.6k Downloads
Part of the CMS Books in Mathematics book series (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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© Springer International Publishing AG 2017

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Authors and Affiliations

  • Heinz H. Bauschke
    • 1
  • Patrick L. Combettes
    • 2
  1. 1.Department of MathematicsUniversity of British ColumbiaKelownaCanada
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA

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