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Finding a Zero of The Sum of Two Maximal Monotone Operators

Author

Listed:
  • A. Moudafi

    (Université Cadi Ayyad
    Université de Limoges)

  • M. Théra

    (Université de Limoges)

Abstract

In this paper, the equivalence between variational inclusions and a generalized type of Weiner–Hopf equation is established. This equivalence is then used to suggest and analyze iterative methods in order to find a zero of the sum of two maximal monotone operators. Special attention is given to the case where one of the operators is Lipschitz continuous and either is strongly monotone or satisfies the Dunn property. Moreover, when the problem has a nonempty solution set, a fixed-point procedure is proposed and its convergence is established provided that the Brézis–Crandall–Pazy condition holds true. More precisely, it is shown that this allows reaching the element of minimal norm of the solution set.

Suggested Citation

  • A. Moudafi & M. Théra, 1997. "Finding a Zero of The Sum of Two Maximal Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 425-448, August.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:2:d:10.1023_a:1022643914538
    DOI: 10.1023/A:1022643914538
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    References listed on IDEAS

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    1. Stephen M. Robinson, 1992. "Normal Maps Induced by Linear Transformations," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 691-714, August.
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