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Contributions à la discretisation des contraintes de mesurabilité pour les problèmes d'optimisation stochastique

Abstract : Our attention has been concentrated on various aspects of stochastic
optimization problems which, according to our knowledge, have not been
studied enough.
Therefore first we shall be interested in the problem relative to the
dual effect, afterwards in the discretization of the measurability
constraints, in static information problem's numerical resolution
and finally we shall study a stochastic optimization problem's optimality
conditions with the purpose of searching for a better
comprehension of the way which intervenes the measurability constraint
in the optimal solution(s) characterization.
Our problem's numerical approach is original of two points of view :
it uses (the) topologies over the space of sigma-fields in order to
measure the information loss ought to the measurability constraint's
discretization . Furthermore the study of this space has brought in new
results which constitue essential elements of our research.
We show that the discretization error results from the contribution of two other
error terms : one resulting from the discretization of the measurability
constraint and of another resulting from the approximation of the
expectation.
In this paper we give asymptotical convergence results of a series
of discrete problems towards the original problem.
For the same particular problem we obtain as well Lipschitz type
results over the value function. Moreover by studying the optimality
conditions we obtain two different possible ways of approaching a
stochastic optimal control problem
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Theses
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https://pastel.archives-ouvertes.fr/tel-00008867
Contributor : Kengy Barty <>
Submitted on : Friday, March 25, 2005 - 11:04:07 AM
Last modification on : Friday, October 23, 2020 - 4:38:15 PM
Long-term archiving on: : Friday, April 2, 2010 - 9:54:09 PM

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  • HAL Id : tel-00008867, version 1

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Kengy Barty. Contributions à la discretisation des contraintes de mesurabilité pour les problèmes d'optimisation stochastique. Mathématiques [math]. Ecole des Ponts ParisTech, 2004. Français. ⟨tel-00008867⟩

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