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Zeros of Sums of Monotone Operators

  • Heinz H. Bauschke
  • Patrick L. Combettes
Chapter
Part of the CMS Books in Mathematics book series (CMSBM)

Abstract

Properties of the zeros of a single monotone operator were discussed in Section  23.4. In this chapter, we first characterize the zeros of sums of monotone operators and then present basic algorithms to construct such zeros iteratively. Duality for monotone inclusion problems is also discussed. In the case of two operators A and B such that A + B is maximally monotone, a point in \({\operatorname {zer}}(A+B)\) could in principle be constructed via Theorem  23.41. However, this approach is numerically viable only when it is easy to compute Jγ(A+B). A more widely applicable alternative is to devise an operator splitting algorithm, in which the operators A and B are employed in separate steps. Various such algorithms are discussed in this chapter.

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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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