Abstract

We present an iterative method for finding zeroes of maximal monotone operators in a real Hilbert space. The underlying idea relies upon the discretization of a first order dissipative dynamical system which allows us to preserve the local feature, as well as to obtain convergence results. The main theorems do not only recover known convergence results of standard and inertial proximal methods, but also provide a theoretical basis for the application of new iterative methods.

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Keywords

  • Monotone operators
  • standard and inertial proximal methods
  • minimization

Mathematics Subject Classification

49J53, 65K10; 49M37, 90C25

References

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Suggested citation

P.-E. Maingé, A. Moudafi. “A Proximal Method for Maximal Monotone Operators via Discretization of a First Order Dissipative Dynamical System.” Journal of Convex Analysis 14 (2007), No. 4, 869–878. https://doi.org/10.68381/jca14049

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Published by Heldermann Verlag, 2007. Rights now held by Banach Press LLC.