Parallel syncrhronous algorithm for nonlinear fixed point problems
DOI:
https://doi.org/10.4067/S0716-09172004000300004Keywords:
Asynchronous algorithm, nonlinear problems, fixed point, monotone operators, convex analysis, algoritmo asíncrono, problemas no-lineales, punto fijo, operadores monótonos, análisis convexo.Abstract
We give in this paper a convergence result concerning parallel synchronous algorithm for nonlinear fixed point problems with respect to the euclidean norm in R?. We then apply this result to some problems related to convex analysis like minimization of functionals, calculus of saddle point, convex programming.References
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[2] J. Bahi, Algorithmes paralleles asynchrones pour des systemes singuliers, Comptes Rendus a l’Académie des Sciences, t. 326, série 1, pp. 1421-1425, (1998).
[3] J. Bahi, Parallel chaotic algorithms for singular linear systems, Parallel Algorithms And Applications, vol. 14, pp. 19-35, (1999).
[4] M.N. El Tarazi, Somme convergence results for asynchronous algorithms, Numer. Math. 39, pp. 325-340, (1982).
[5] F.J. Luque, Asymptotic convergence analysis of the proximal point algorithm, SIAM J. Control And Optimization, Vol. 22, No. 2, pp. 277-293, (1984).
[6] R.T. Rockafellar, Convex Analysis, Princeton University Press. (1970).
[7] R.T. Rockafellar, Monotone operators associated with saddle functions and minimax problems, in Nonlinear Functional Analysis, vol. 18 part 1, Amer. Math. Soc., pp. 397-407, (1970).
[8] R.T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc., 149, pp. 75-88, (1970).
[9] R.T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control And Optimization, Vol. 14, No. 5, pp. 877-898, (1976).
[10] R.T. Rockafellar, Augmented Lagrangians and application of the proximal point algorithm in convex programming, Math. Oper. Res., 1, pp. 97-116, (1976).
Published
2017-05-22
How to Cite
[1]
A. Addou and A. Benahmed, “Parallel syncrhronous algorithm for nonlinear fixed point problems”, Proyecciones (Antofagasta, On line), vol. 23, no. 3, pp. 241-252, May 2017.
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