Stochastic Approximation Method for Fixed Point Problems

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References

[1] M. T. Wasan, “Stochastic Approximation,” Cambridge University Press, Cambridge, 1969.

[2] M. B. Nevelson and R. Z. Hasminsky, “Stochastic Approximation and Recursive Estimation,” AMS Providence, Rhode Island, 1973.

[3] Ya. Alber and S. Shilman, “Nonasymptotic Estimates of the Convergence Rate of Stochastic Iterative Algorithms,” Automation and Remote Control, Vol. 42, 1981, pp. 32-41.

[4] Ya. Alber and S. Shilman, “General Nonasymptotic Estimates of the Convergence Rate of Iterative Stochastic Algorithms,” USSR Computational Mathematics and Mathematical Physics, Vol. 25, No. 2, 1985, pp. 13-20.
doi:10.1016/0041-5553(85)90099-0

[5] K. Barty, J.-S. Roy and C. Strugarek, “Hilbert-Valued Perturbed Subgradient Algorithms,” Mathematics of Operation Research, Vol. 32, No. 3, 2007, pp. 551-562.
doi:10.1287/moor.1070.0253

[6] X. Chen and H. White, “Asymptotic Properties of Some Projection-Based Robbins-Monro Procedures in a Hilbert Space,” Studies in Nonlinear Dynamics & Econometrics, Vol. 6, No. 1, 2002, pp. 1-53.
doi:10.2202/1558-3708.1000

[7] Ya. I. Alber and A. N. Iusem, “Extension of Subgradient Techniques for Nonsmooth Optimization in Banach Spaces,” Set-Valued Analysis, Vol. 9, No. 4, 2001, pp. 315-335. doi:10.1023/A:1012665832688

[8] Ya. Alber, A. Iusem and M. Solodov, “On the Projection Subgradient Method for Nonsmooth Convex Optimization in a Hilbert Space,” Mathematical Programming, Vol. 81, No. 1, 1998, pp. 23-35.
doi:10.1007/BF01584842

[9] A. P. Dempster, N. M. Laird and D. B. Rubin, “Maximal Likelihood from Incomplete Data via the EM Algorithm,” Journal of the Royal Statistical Society, Vol. 39, No. 1, 1977, pp. 185-197.

[10] W. Rudin, “Real and Complex Analysis,” McGraw-Hill, New York, 1978.

[11] Ya. I. Alber and S. Guerre-Delabriere, “Principle of Weakly Contractive Maps in Hilbert Spaces,” Operator Theory, Advances and Applications, Vol. 98, 1997, pp. 7-22.

[12] Ya. I. Alber, “Recurrence Relations and Variational Inequalities,” Soviet Mathematics Doklady, Vol. 27, 1983, pp. 511-517.

[13] Ya. Alber, S. Guerre-Delabriere and L. Zelenko, “The Principle of Weakly Contractive Maps in Metric Spaces,” Communications on Applied Nonlinear Analysis, Vol. 5, No. 1, 1998, pp. 45-68.

[14] Ya. I. Alber, “New Results in Fixed Point Theory,” Preprint, Haifa Technion, 2000.

[15] J. Diestel, “The Geometry of Banach Spaces,” Lecture Notes in Mathematics, No. 485, Springer, Berlin, 1975.

[16] T. Figiel, “On the Moduli of Convexity and Smoothness,” Studia Mathematica, Vol. 56, No. 2, 1976, pp. 121-155.

[17] Ya. Alber and I. Ryazantseva, “Nonlinear Ill-Posed Problems of Monotone Type,” Springer, Berlin, 2006.

[18] M. Métivier, “Semimartingales,” De Gruyter, Berlin, 1982.
doi:10.1515/9783110845563