Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters
We consider the numerical approximation of an optimal control problem for an elliptic Partial
Differential Equation (PDE) with random coefficients. Specifically, the control function is a
deterministic, distributed forcing term that minimizes the expected squared L 2 misfit
between the state (ie solution to the PDE) and a target function, subject to a regularization
for well posedness. For the numerical treatment of this risk-averse Optimal Control Problem
(OCP) we consider a Finite Element discretization of the underlying PDE, a Monte Carlo …
Differential Equation (PDE) with random coefficients. Specifically, the control function is a
deterministic, distributed forcing term that minimizes the expected squared L 2 misfit
between the state (ie solution to the PDE) and a target function, subject to a regularization
for well posedness. For the numerical treatment of this risk-averse Optimal Control Problem
(OCP) we consider a Finite Element discretization of the underlying PDE, a Monte Carlo …
[PDF][PDF] Analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters
We consider the numerical approximation of a risk-averse optimal control problem for an
elliptic partial differential equation (PDE) with random coefficients. Specifically, the control
function is a deterministic, distributed forcing term that minimizes the expected mean
squared distance between the state (ie solution to the PDE) and a target function, subject to
a regularization for well posedness. For the numerical treatment of this riskaverse optimal
control problem, we consider a Finite Element discretization of the underlying PDEs, a …
elliptic partial differential equation (PDE) with random coefficients. Specifically, the control
function is a deterministic, distributed forcing term that minimizes the expected mean
squared distance between the state (ie solution to the PDE) and a target function, subject to
a regularization for well posedness. For the numerical treatment of this riskaverse optimal
control problem, we consider a Finite Element discretization of the underlying PDEs, a …
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