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doctoral thesis

Stochastic approximation methods for PDE constrained optimal control problems with uncertain parameters

Martin, Matthieu Claude  
2019

This thesis work focuses on optimal control of partial differential equations (PDEs) with uncertain parameters, treated as a random variables. In particular, we assume that the random parameters are not observable and look for a deterministic control which is robust with respect to the randomness. The theoretical framework is based on adjoint calculus to compute the gradient of the objective functional. Unlike the deterministic case, we have a set of PDEs indexed by some uncertain parameters and the objective functional we consider includes some risk measure (e.g. expectation, variance, quantile (Value at Risk), ...) to take care of all realizations of our uncertain parameters. Introducing the regular class of coherent risk measure, results of convergence and regularity of the optimal control have been derived.

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Type
doctoral thesis
DOI
10.5075/epfl-thesis-7233
Author(s)
Martin, Matthieu Claude  
Advisors
Nobile, Fabio  
Jury

Prof. Friedrich Eisenbrand (président) ; Prof. Fabio Nobile (directeur de thèse) ; Prof. Marco Picasso, Prof. Elisabeth Ullmann, Prof. Stefan Vandewalle (rapporteurs)

Date Issued

2019

Publisher

EPFL

Publisher place

Lausanne

Public defense year

2019-03-22

Thesis number

7233

Total of pages

189

Subjects

PDE constrained optimization

•

risk-averse optimal control

•

optimiza-tion under uncertainty

•

PDE with random coefficients

•

stochastic approximation

•

stochastic gradient

•

Monte Carlo

•

SAG

•

SAGA

•

importance sampling

EPFL units
CSQI  
Faculty
SB  
School
MATHICSE  
Doctoral School
EDMA  
Available on Infoscience
March 13, 2019
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/155533
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