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On an Iterative Method for Finding a Zero to the Sum of Two Maximal Monotone Operators

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Listed:
  • Hongwei Jiao
  • Fenghui Wang

Abstract

In this paper we consider a problem that consists of finding a zero to the sum of two monotone operators. One method for solving such a problem is the forward‐backward splitting method. We present some new conditions that guarantee the weak convergence of the forward‐backward method. Applications of these results, including variational inequalities and gradient projection algorithms, are also considered.

Suggested Citation

  • Hongwei Jiao & Fenghui Wang, 2014. "On an Iterative Method for Finding a Zero to the Sum of Two Maximal Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:414031
    DOI: 10.1155/2014/414031
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    References listed on IDEAS

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    1. Genaro López & Victoria Martín-Márquez & Fenghui Wang & Hong-Kun Xu, 2012. "Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, July.
    2. Genaro López & Victoria Martín-Márquez & Fenghui Wang & Hong-Kun Xu, 2012. "Forward‐Backward Splitting Methods for Accretive Operators in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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