B. Delyon. Stochastic approximation with decreasing gain: convergence and asymptotic theory. Unpublished lecture notes, Université de Rennes, 2000.

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1 Some References

2 Laetitia Andrieu, Guy Cohen and Felisa J. Vázquez-Abad. Gradient-based simulation optimization under probability constraints. European Journal of Operational Research, 212, , A. Benveniste, M. Métivier, and P. Priouret. Adaptative Algorithms and Stochastic Approximation. Springer Verlag, B. Delyon. Stochastic approximation with decreasing gain: convergence and asymptotic theory. Unpublished lecture notes, Université de Rennes, M. Duflo. Algorithmes stochastiques. Springer Verlag, M. Duflo. Random Iterative Models. Springer Verlag, J. Kiefer and J. Wolfowitz. Stochastic estimation of the maximum of a regression function. Annals of Mathematical Statistics, 23: , H. J. Kushner and D. S. Clark. Stochastic Approximation Methods for Constrained and Unconstrained Systems. Springer Verlag, 1978.

3 T. L. Lai. Stochastic approximation. The Annals of Statistics, 31(2): , B. T. Polyak. Convergence and convergence rate of iterative stochastic algorithms. Automation and Remote Control, 37(12): , B. T. Polyak. New method of stochastic approximation type. Automation and Remote Control, 51(7): , B. T. Polyak and A. B. Juditsky. Acceleration of stochastic approximation by averaging. SIAM Journal on Control and Optimization, 30(4): , H. Robbins and S. Monro. A stochastic approximation method. Annals of Mathematical Statistics, 22: , 1951.

4 I. Ekeland and R. Temam. Convex analysis and variational problems. North Holland, Amsterdam, R. T. Rockafellar and R. J.-B. Wets. Variational Analysis, volume 317 of A series of Comprehensive Studies in Mathematics. Springer Verlag, 1998.

5 P. Carpentier, G. Cohen, and J.-C. Culioli. Stochastic optimal control and decomposition-coordination methods Part I: Theory. In: Recent Developments in Optimization, Roland Durier and Christian Michelot (Eds.), LNEMS 429:72-87, Springer-Verlag, Berlin, G. Cohen. Optimisation des grands systèmes. Unpublished lecture notes, DEA MMME, Université Paris I Panthéon-Sorbonne, J.-C. Culioli. Algorithmes de décomposition/coordination en optimisation stochastique. PhD thesis, École Nationale Supérieure des Mines de Paris, J.-C. Culioli and G. Cohen. Decomposition-coordination algorithms in stochastic optimization. SIAM Journal on Control and Optimization, 28(6): , J.-C. Culioli and G. Cohen. Optimisation stochastique sous contraintes en espérance. CRAS, t.320, Série I, pp , 1995.

6 K. Barty, P. Carpentier, J.-P. Chancelier, G. Cohen, M. De Lara, and T. Guilbaud. Dual effect free stochastic controls. Annals of Operation Research, 142(1):41 62, February J. Dubra and F. Echenique. Information is not about measurability. Mathematical Social Sciences, 47(2): , Y. C. Ho and K. C. Chu. Information structure in dynamic multi-person control problems. Automatica, 10: , 1974.

7 K. Barty. Contributions à la discrétisation des contraintes de mesurabilité, pour les problèmes d optimisation stochastique. PhD thesis, École Nationale des Ponts et Chaussées, A. Gersho and R. M. Gray. Vector Quantization and Signal Compression. Kluwer Academic Publishers, H. Kudo. A note on the strong convergence of σ-algebras. Annals of Probability, 2(1):76 83, T. Pennanen. Epi-convergent discretizations of multistage stochastic programs. Mathematics of Operations Research, 30(1): , 2005.

8 J. Dupacova and R. J. Wets. Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems. The Annals of Statistics, 16(4): , A. King and R. J.-B. Wets. Epi-consistency of convex stochastic programs. Stochastics and Stochastics Reports, 34:83 92, A. Shapiro. On complexity of multistage stochastic programs. Operations Research Letters, 34-1:1 8, A. Shapiro, D. Dentcheva, and A. Ruszczyński. Lectures on Stochastic Programming: Modeling and Theory. SIAM, Philadelphia, 2009.

9 Y. C. Ho. Review of the Witsenhausen problem. In 47th IEEE Conference on Decision and Control, CDC 2008, pages , December H. S. Witsenhausen. A counterexample in stochastic optimal control. SIAM Journal on Control, 6(1): , 1968.

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