5 papers
A randomized operator splitting scheme inspired by stochastic optimization methods
Monika Eisenmann, Tony Stillfjord
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination…
Sub-linear convergence of a tamed stochastic gradient descent method in Hilbert space
Monika Eisenmann, Tony Stillfjord
In this paper, we introduce the tamed stochastic gradient descent method (TSGD) for optimization problems. Inspired by the tamed Euler scheme, which is a commonly used method withi…
Sub-linear convergence of a stochastic proximal iteration method in Hilbert space
Monika Eisenmann, Tony Stillfjord, Måns Williamson
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the…
A variational approach to the sum splitting scheme
Monika Eisenmann, Eskil Hansen
Nonlinear parabolic equations are frequently encountered in applications and efficient approximating techniques for their solution are of great importance. In order to provide an e…
Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data
Monika Eisenmann, Etienne Emmrich, Volker Mehrmann
For initial value problems associated with operator-valued Riccati differential equations posed in the space of Hilbert--Schmidt operators existence of solutions is studied. An exi…