La Fondation Hadamard et Digiteo se sont associés le 6 mai 2014 pour organiser un séminaire autour de Georg Pflug, de l’Université de Vienne : "Multistage stochastic optimization : Approximations, bounds and time consistency".
Le séminaire a eu lieu à l’École Polytechnique dans l’amphithéâtre Alfred SAUVY.
We discuss two aspects of multistage stochastic optimization. In the first part we present several results about approximations of large or even huge problems by simpler ones. The basic continuity result is based on convexity arguments and the notion of the nested distance between scenario processes. We derive
upper and lower bounds for the solution of multistage programs and
illustrate them with some examples.
In the second part of the talk we give a rigorous definition of the time consistency property for risk functionals and for multistage decision problems. We characterize time-consistent functionals. A main result states that non-time consistent decision problem can be made time consistent by enlarging the decision space and replacing
the original problem by a minimax problem.
Finally examples from optimal management of thermo and hydro-electricity plants are presented. If there is time also pricing principles for flexible energy delivery contracts based on multistage stochastic bilevel optimization are discussed.