Viscosity Approximation Methods for Fixed-Points Problems

@article{Moudafi2000ViscosityAM,
  title={Viscosity Approximation Methods for Fixed-Points Problems},
  author={Abdellatif Moudafi},
  journal={Journal of Mathematical Analysis and Applications},
  year={2000},
  volume={241},
  pages={46-55}
}
  • A. Moudafi
  • Published 2000
  • Mathematics
  • Journal of Mathematical Analysis and Applications
The aim of this work is to propose viscosity approximation methods which amounts to selecting a particular fixed-point of a given nonexpansive self-mapping. 
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666 Citations
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References

SHOWING 1-10 OF 20 REFERENCES

Produits infinis de resolvantes

This paper is concerned with the convergence of the sequence χn=(I+λnA)−1χn−1 whereA is maximal monotone and λn>0. Various assumptions onA and λn are considered.

Viscosity Solutions of Minimization Problems

It is proved, in a rather large setting, that the solutions of the approximate problems converge to a ``viscosity solution'' of the original problem, that is, a solution that is minimal among all the solutions with respect to some viscosity criteria.

A Dynamical Approach to Convex Minimization Coupling Approximation with the Steepest Descent Method

We study the asymptotic behavior of the solutions to evolution equations of the form 0 # u* (t)+f(u(t), =(t)); u(0)=u0, where [f (}, =): =>0] is a family of strictly convex functions whose minimum is…

Asymptotic analysis of the exponential penalty trajectory in linear programming

The primal trajectory has an asymptotic ray and the dual trajectory converges to an interior dual feasible solution, which converges exponentially fast to a particular dual optimal solution.

Convergence of convex sets and of solutions of variational inequalities

Two remarks on the convergence of convex functions and monotone operators

Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert

Rafle par un Convexe Variable,’

  • Seminaire d’Analyse Convexe, Montpeĺ lier, expose,
  • 1971

Problems of Fixed Point Theory in Hilbert and Banach Spaces

  • Lecture

ѨrѨ n denotes the exterior normal derivative