Some References P. Carpentier Master MMMEF Cours MNOS 2014-2015 - PowerPoint PPT Presentation

Stochastic Approximation and Stochastic Gradient Optimization Theory and Large Scale Systems Dual Effect and Discretization Stochastic Programming and Stochastic Optimal Control Some References P. Carpentier Master MMMEF — Cours MNOS 2014-2015 263 / 263

Stochastic Approximation and Stochastic Gradient Optimization Theory and Large Scale Systems Dual Effect and Discretization Stochastic Programming and Stochastic Optimal Control Laetitia Andrieu, Guy Cohen and Felisa J. V´ azquez-Abad. Gradient-based simulation optimization under probability constraints. European Journal of Operational Research , 212, 345-351, 2011. A. Benveniste, M. M´ etivier, and P. Priouret. Adaptative Algorithms and Stochastic Approximation . Springer Verlag, 1990. B. Delyon. Stochastic approximation with decreasing gain: convergence and asymptotic theory. Unpublished lecture notes, Universit´ e de Rennes, 2000. M. Duflo. Algorithmes stochastiques . Springer Verlag, 1996. M. Duflo. Random Iterative Models . Springer Verlag, 1997. J. Kiefer and J. Wolfowitz. Stochastic estimation of the maximum of a regression function. Annals of Mathematical Statistics , 23:462–466, 1952. H. J. Kushner and D. S. Clark. Stochastic Approximation Methods for Constrained and Unconstrained Systems . Springer Verlag, 1978. P. Carpentier Master MMMEF — Cours MNOS 2014-2015 263 / 263

Stochastic Approximation and Stochastic Gradient Optimization Theory and Large Scale Systems Dual Effect and Discretization Stochastic Programming and Stochastic Optimal Control T. L. Lai. Stochastic approximation. The Annals of Statistics , 31(2):391–406, 2003. B. T. Polyak. Convergence and convergence rate of iterative stochastic algorithms. Automation and Remote Control , 37(12):1858–1868, 1976. B. T. Polyak. New method of stochastic approximation type. Automation and Remote Control , 51(7):937–946, 1990. B. T. Polyak and A. B. Juditsky. Acceleration of stochastic approximation by averaging. SIAM Journal on Control and Optimization , 30(4):838–855, 1992. H. Robbins and S. Monro. A stochastic approximation method. Annals of Mathematical Statistics , 22:400–407, 1951. P. Carpentier Master MMMEF — Cours MNOS 2014-2015 263 / 263

Stochastic Approximation and Stochastic Gradient Optimization Theory and Large Scale Systems Dual Effect and Discretization Stochastic Programming and Stochastic Optimal Control I. Ekeland and R. Temam. Convex analysis and variational problems . North Holland, Amsterdam, 1976. R. T. Rockafellar and R. J.-B. Wets. Variational Analysis , volume 317 of A series of Comprehensive Studies in Mathematics . Springer Verlag, 1998. P. Carpentier Master MMMEF — Cours MNOS 2014-2015 263 / 263

Stochastic Approximation and Stochastic Gradient Optimization Theory and Large Scale Systems Dual Effect and Discretization Stochastic Programming and Stochastic Optimal Control 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 , 1995. G. Cohen. Optimisation des grands syst` emes. Unpublished lecture notes, DEA MMME, Universit´ e Paris I Panth´ eon-Sorbonne, 2004. http://cermics.enpc.fr/~cohen-g/documents/ParisIcours-A4-NB.pdf . J.-C. Culioli. Algorithmes de d´ ecomposition/coordination en optimisation stochastique . PhD thesis, ´ Ecole Nationale Sup´ erieure des Mines de Paris, 1987. J.-C. Culioli and G. Cohen. Decomposition-coordination algorithms in stochastic optimization. SIAM Journal on Control and Optimization , 28(6):1372–1403, 1990. J.-C. Culioli and G. Cohen. Optimisation stochastique sous contraintes en esp´ erance. CRAS , t.320, S´ erie I, pp. 75-758, 1995. P. Carpentier Master MMMEF — Cours MNOS 2014-2015 263 / 263

Stochastic Approximation and Stochastic Gradient Optimization Theory and Large Scale Systems Dual Effect and Discretization Stochastic Programming and Stochastic Optimal Control 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 2006. J. Dubra and F. Echenique. Information is not about measurability. Mathematical Social Sciences , 47(2):177–185, 2004. Y. C. Ho and K. C. Chu. Information structure in dynamic multi-person control problems. Automatica , 10:341–351, 1974. P. Carpentier Master MMMEF — Cours MNOS 2014-2015 263 / 263

Stochastic Approximation and Stochastic Gradient Optimization Theory and Large Scale Systems Dual Effect and Discretization Stochastic Programming and Stochastic Optimal Control K. Barty. Contributions ` a la discr´ etisation des contraintes de mesurabilit´ e, pour les probl` emes d’optimisation stochastique . PhD thesis, ´ Ecole Nationale des Ponts et Chauss´ ees, 2004. http://cermics.enpc.fr/theses . A. Gersho and R. M. Gray. Vector Quantization and Signal Compression . Kluwer Academic Publishers, 1992. H. Kudo. A note on the strong convergence of σ -algebras. Annals of Probability , 2(1):76–83, 1974. T. Pennanen. Epi-convergent discretizations of multistage stochastic programs. Mathematics of Operations Research , 30(1):245–256, 2005. P. Carpentier Master MMMEF — Cours MNOS 2014-2015 263 / 263

Stochastic Approximation and Stochastic Gradient Optimization Theory and Large Scale Systems Dual Effect and Discretization Stochastic Programming and Stochastic Optimal Control 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):1517–1549, 1988. A. King and R. J.-B. Wets. Epi-consistency of convex stochastic programs. Stochastics and Stochastics Reports , 34:83–92, 1991. A. Shapiro. On complexity of multistage stochastic programs. Operations Research Letters , 34-1:1–8, 2006. A. Shapiro, D. Dentcheva, and A. Ruszczy´ nski. Lectures on Stochastic Programming: Modeling and Theory . SIAM, Philadelphia, 2009. P. Carpentier Master MMMEF — Cours MNOS 2014-2015 263 / 263

Stochastic Approximation and Stochastic Gradient Optimization Theory and Large Scale Systems Dual Effect and Discretization Stochastic Programming and Stochastic Optimal Control Y. C. Ho. Review of the Witsenhausen problem. In 47th IEEE Conference on Decision and Control, 2008. CDC 2008 , pages 1611–1613, December 2008. H. S. Witsenhausen. A counterexample in stochastic optimal control. SIAM Journal on Control , 6(1):131–147, 1968. P. Carpentier Master MMMEF — Cours MNOS 2014-2015 263 / 263