27 citations · 49 across the 14 of their papers we have counts for
17 papers
Sample-Based Consistency in Infinite-Dimensional Conic-Constrained Stochastic Optimization
Caroline Geiersbach, Johannes Milz
This paper is concerned with a class of stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. For this class of problems, we investiga…
A Cournot-Nash Model for a Coupled Hydrogen and Electricity Market
Pavel Dvurechensky, Caroline Geiersbach, Michael Hintermüller +3
We present a novel model of a coupled hydrogen and electricity market on the intraday time scale, where hydrogen gas is used as a storage device for the electric grid. Electricity…
Two-norm discrepancy and convergence of the stochastic gradient method with application to shape optimization
Marc Dambrine, Caroline Geiersbach, Helmut Harbrecht
The present article is dedicated to proving convergence of the stochastic gradient method in case of random shape optimization problems. To that end, we consider Bernoulli's exteri…
Numerical solution of an optimal control problem with probabilistic and almost sure state constraints
Caroline Geiersbach, René Henrion, Pedro Pérez-Aros
We consider the optimal control of a PDE with random source term subject to probabilistic or almost sure state constraints. In the main theoretical result, we provide an exact form…
Optimization of piecewise smooth shapes under uncertainty using the example of Navier-Stokes flow
Caroline Geiersbach, Tim Suchan, Kathrin Welker
We investigate a complex system involving multiple shapes to be optimized in a domain, taking into account geometric constraints on the shapes and uncertainty appearing in the phys…
Optimality conditions in control problems with random state constraints in probabilistic or almost-sure form
Caroline Geiersbach, René Henrion
In this paper, we discuss optimality conditions for optimization problems involving random state constraints, which are modeled in probabilistic or almost sure form. While the latt…
Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds
Caroline Geiersbach, Tim Suchan, Kathrin Welker
In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite…
Risk-averse optimal control of random elliptic variational inequalities
Amal Alphonse, Caroline Geiersbach, Michael Hintermüller +1
We consider a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. By deriving KKT-type optimality conditions for a pen…
A stochastic gradient method for a class of nonlinear PDE-constrained optimal control problems under uncertainty
Caroline Geiersbach, Teresa Scarinci
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in eng…
Optimality Conditions and Moreau--Yosida Regularization for Almost Sure State Constraints
Caroline Geiersbach, Michael Hintermüller
We analyze a potentially risk-averse convex stochastic optimization problem, where the control is deterministic and the state is a Banach-valued essentially bounded random variable…
PDE-constrained shape optimization: towards product shape spaces and stochastic models
Caroline Geiersbach, Estefania Loayza-Romero, Kathrin Welker
Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional i…
Optimality Conditions for Convex Stochastic Optimization Problems in Banach Spaces with Almost Sure State Constraints
Caroline Geiersbach, Winnifried Wollner
We analyze a convex stochastic optimization problem where the state is assumed to belong to the Bochner space of essentially bounded random variables with images in a reflexive and…
Stochastic approximation for optimization in shape spaces
Caroline Geiersbach, Estefania Loayza-Romero, Kathrin Welker
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-di…
Stochastic Proximal Gradient Methods for Nonconvex Problems in Hilbert Spaces
Caroline Geiersbach, Teresa Scarinci
For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems…
A Stochastic Gradient Method with Mesh Refinement for PDE Constrained Optimization under Uncertainty
Caroline Geiersbach, Winnifried Wollner
Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on th…
Computational Aspects for Interface Identification Problems with Stochastic Modelling
Caroline Geiersbach, Estefania Loayza, Kathrin Welker
In this paper, a shape optimization problem constrained by a random elliptic partial differential equation with a pure Neumann boundary is presented. The model is motivated by appl…
Projected Stochastic Gradients for Convex Constrained Problems in Hilbert Spaces
Caroline Geiersbach, Georg Pflug
Convergence of a projected stochastic gradient algorithm is demonstrated for convex objective functionals with convex constraint sets in Hilbert spaces. In the convex case, the seq…