1 citations · 1 across the 2 of their papers we have counts for
6 papers
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…
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…
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…
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…