Barty, Kengy (2004) Discretization of measurability constraints for stochastic optimization problems. PhD thesis Mathématiques et informatique, ENPC.
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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 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.
| Item Type: | PhD Thesis (PhD) |
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| Thesis Supervisor: | Cohen, Guy |
| Date: | June 2004 |
| Board of examiners: | Bonnisseau, J.m. and Quadrat, J.p. and Hiriart-Urruty, J.b. and Bouleau, Nicolas and Aïd, R. and Cohen, Guy |
| Discipline: | Mathématiques et informatique |
| Collection (Fonds): | ENPC |
| Institution: | ENPC |
| Subjects: | 2. Information and Communication Sciences and Technologies 1. Mathematics and Applications |
| Uncontrolled Keywords: | Optimisation stochastique, Contrainte de mesurabilité, Quantification |
| ID Code: | 921 |
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| Deposited By: | Christiane Baudry |
| Deposited On: | 29 November 2004 |
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