Dynamical Behavior of a Stochastic Forward–Backward Algorithm Using Random Monotone Operators

@article{Bianchi2016DynamicalBO,
  title={Dynamical Behavior of a Stochastic Forward–Backward Algorithm Using Random Monotone Operators},
  author={Pascal Bianchi and Walid Hachem},
  journal={Journal of Optimization Theory and Applications},
  year={2016},
  volume={171},
  pages={90-120}
}
  • Pascal Bianchi, Walid Hachem
  • Published 2016
  • Mathematics, Computer Science
  • Journal of Optimization Theory and Applications
  • The purpose of this paper is to study the dynamical behavior of the sequence produced by a Forward–Backward algorithm, involving two random maximal monotone operators and a sequence of decreasing step sizes. Defining a mean monotone operator as an Aumann integral and assuming that the sum of the two mean operators is maximal (sufficient maximality conditions are provided), it is shown that with probability one, the interpolated process obtained from the iterates is an asymptotic… CONTINUE READING

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