A convergence result for asynchronous algorithms and applications
DOI:
https://doi.org/10.4067/S0716-09172007000200005Keywords:
Asynchronous algorithm, Nonlinear problems, Monotone operators, Fixed point, Optimization problem, Variational inequality problem, Convex analysis.Abstract
We give in this paper a convergence result concerning parallel asynchronous algorithm with bounded delays to solve a nonlinear fixed point problems. This result is applied to calculate the solution of a strongly monotone operator. Special cases of these operators are used to solve some problems related to convex analysis like minimization of functionals, calculus of saddle point and variational inequality problem.
References
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[10] R. T. Rockafellar, Convex Analysis, Princeton Univ. Press, (1970).
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[12] R. T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc., 149, pp. 75-88, (1970).
[13] R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., Vol. 14, No. 5, pp. 877-898, (1976).
[2] J. Bahi, Asynchronous iterative algorithms for nonexpansive linear systems, Parallel And Distributed Computing, vol. 60, no. 1, pp. 92-112, (2000).
[3] G. M. Baudet, Asynchronous iterative methods for multiprocessors, J. ACM, 25, pp. 226-244, (1978).
[4] D. P. Bertsekast, J. Tsitsiklis, Some aspects of parallel and distributed iterative algorihms-A survey, Automatica, vol. 27, no.1, pp. 3-21, (1991).
[5] D. Chazan, W. L. Miranker, Chaotic relaxation, Linear Algebra Appl. 2, pp. 199-222, (1969).
[6] M. N. El Tarazi, Somme convergence results for asynchronous algorithms, Numer. Math. 39, pp. 325-340, (1982).
[7] D. H. Griffel, Applied Functional Analysis, Wiley (1981).
[8] J. C. Miellou, Algorithmes de relaxation chaotiques ` a retard, RAIRO (R1), pp. 55-82, (1975).
[9] R. R. Phelps, Lectures on maximal monotone operators, arXiv: math. FA /9302209 v1, (1993).
[10] R. T. Rockafellar, Convex Analysis, Princeton Univ. Press, (1970).
[11] 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).
[12] R. T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc., 149, pp. 75-88, (1970).
[13] R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., Vol. 14, No. 5, pp. 877-898, (1976).
Published
2017-04-18
How to Cite
[1]
A. Benahmed, “A convergence result for asynchronous algorithms and applications”, Proyecciones (Antofagasta, On line), vol. 26, no. 2, pp. 219-236, Apr. 2017.
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