Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration
We study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal
control problems subject to parabolic partial differential equation (PDE) constraints under …
control problems subject to parabolic partial differential equation (PDE) constraints under …
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 …
Differential Equation (PDE) with random coefficients. Specifically, the control function is a …
An efficient ADAM-type algorithm with finite elements discretization technique for random elliptic optimal control problems
H Song, H Wang, J Wu, J Yang - Journal of Computational and Applied …, 2025 - Elsevier
We consider an optimal control problem governed by an elliptic partial differential equation
(PDE) with random coefficient, and introduce an efficient numerical method for the problem …
(PDE) with random coefficient, and introduce an efficient numerical method for the problem …
A relaxation-based probabilistic approach for PDE-constrained optimization under uncertainty with pointwise state constraints
We consider a class of convex risk-neutral PDE-constrained optimization problems subject
to pointwise control and state constraints. Due to the many challenges associated with …
to pointwise control and state constraints. Due to the many challenges associated with …
Multilevel optimization for inverse problems
Inverse problems occur in a variety of parameter identification tasks in engineering. Such
problems are challenging in practice, as they require repeated evaluation of computationally …
problems are challenging in practice, as they require repeated evaluation of computationally …
The continuous stochastic gradient method: part I–convergence theory
In this contribution, we present a full overview of the continuous stochastic gradient (CSG)
method, including convergence results, step size rules and algorithmic insights. We consider …
method, including convergence results, step size rules and algorithmic insights. We consider …
Reliable error estimates for optimal control of linear elliptic PDEs with random inputs
J Milz - SIAM/ASA Journal on Uncertainty Quantification, 2023 - SIAM
We discretize a risk-neutral optimal control problem governed by a linear elliptic partial
differential equation with random inputs using a Monte Carlo sample-based approximation …
differential equation with random inputs using a Monte Carlo sample-based approximation …
Efficient mini-batch stochastic gradient descent with Centroidal Voronoi Tessellation for PDE-constrained optimization under uncertainty
L Chen, M Xiong, J Ming, X He - Physica D: Nonlinear Phenomena, 2024 - Elsevier
The study of optimal control problems under uncertainty plays an important role in scientific
numerical simulations. This class of optimization problems is frequently utilized in …
numerical simulations. This class of optimization problems is frequently utilized in …
An approximation scheme for distributionally robust PDE-constrained optimization
We develop a sampling-free approximation scheme for distributionally robust PDE-
constrained optimization problems, which are min-max control problems. We define the …
constrained optimization problems, which are min-max control problems. We define the …
Tensor train solution to uncertain optimization problems with shared sparsity penalty
We develop both first and second order numerical optimization methods to solve non-
smooth optimization problems featuring a shared sparsity penalty, constrained by differential …
smooth optimization problems featuring a shared sparsity penalty, constrained by differential …