École Nationale Supérieure de
Techniques Avancées

Abstract

The dissertation focuses on stochastic optimization. The first chapter proposes a typology of stochastic optimization problems. The second chapter proves that in the one dimensional case, only systems with linear dynamics and observations are open loop dual effect free. The third chapter enlightens the importance of the information structure of the random process when one aims at discretizing or giving stability results for multistage stochastic programs. The fourth chapter proposes a new family of stochastic algorithms which allow to seek for the optimal control as a function of the uncertainty. The fifth chapter shows the limits and possibilities of decomposition and agreggation for large scale dynamic stochastic programs.