20 citations · 48 across the 14 of their papers we have counts for
14 papers
Convergence analysis of a full discretization of operator-valued differential Riccati equations
Eskil Hansen, Tony Stillfjord, Teodor Åberg
In recent previous work [E. Hansen, T. Stillfjord and T. Åberg, SIAM J. Numer. Anal., to appear], we analyzed the convergence of operator splitting methods applied to operator-valu…
Convergence analysis of Lie and Strang splitting for operator-valued differential Riccati equations
Eskil Hansen, Tony Stillfjord, Teodor Åberg
Differential Riccati equations (DREs) are semilinear matrix- or operator-valued differential equations with quadratic non-linearities. They arise in many different areas, and are p…
Analysis of a Class of Stochastic Component-Wise Soft-Clipping Schemes
Måns Williamson, Monika Eisenmann, Tony Stillfjord
Choosing the optimization algorithm that performs best on a given machine learning problem is often delicate, and there is no guarantee that current state-of-the-art algorithms wil…
Almost sure convergence of stochastic Hamiltonian descent methods
Måns Williamson, Tony Stillfjord
Gradient normalization and soft clipping are two popular techniques for tackling instability issues and improving convergence of stochastic gradient descent (SGD) with momentum. In…
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…
SRKCD: a stabilized Runge-Kutta method for stochastic optimization
Tony Stillfjord, Måns Williamson
We introduce a family of stochastic optimization methods based on the Runge-Kutta-Chebyshev (RKC) schemes. The RKC methods are explicit methods originally designed for solving stif…
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 linear implicit Euler method for the finite element discretization of a controlled stochastic heat equation
Peter Benner, Tony Stillfjord, Christoph Trautwein
We consider a numerical approximation of a linear quadratic control problem constrained by the stochastic heat equation with non-homogeneous Neumann boundary conditions. This invol…
GPU acceleration of splitting schemes applied to differential matrix equations
Hermann Mena, Lena-Maria Pfurtscheller, Tony Stillfjord
We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the fiel…
Singular value decay of operator-valued differential Lyapunov and Riccati equations
Tony Stillfjord
We consider operator-valued differential Lyapunov and Riccati equations, where the operators and may be relatively unbounded with respect to (in the standard notation).…
Multiscale differential Riccati equations for linear quadratic regulator problems
Axel Målqvist, Anna Persson, Tony Stillfjord
We consider approximations to the solutions of differential Riccati equations in the context of linear quadratic regulator problems, where the state equation is governed by a multi…
Adaptive high-order splitting schemes for large-scale differential Riccati equations
Tony Stillfjord
We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field…
Finite element convergence analysis for the thermoviscoelastic Joule heating problem
Axel Målqvist, Tony Stillfjord
We consider a system of equations that model the temperature, electric potential and deformation of a thermoviscoelastic body. A typical application is a thermistor; an electrical…