30 citations · 94 across the 15 of their papers we have counts for
15 papers
Stabilizability for nonautonomous linear parabolic equations with actuators as distributions
Karl Kunisch, Sérgio S. Rodrigues, Daniel Walter
The stabilizability of a general class of abstract parabolic-like equations is investigated, with a finite number of actuators. This class includes the case of actuators given as d…
Towards optimal sensor placement for inverse problems in spaces of measures
Phuoc-Truong Huynh, Konstantin Pieper, Daniel Walter
The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be usefu…
Extremal points and sparse optimization for generalized Kantorovich-Rubinstein norms
Marcello Carioni, José A. Iglesias, Daniel Walter
A precise characterization of the extremal points of sublevel sets of nonsmooth penalties provides both detailed information about minimizers, and optimality conditions in general…
Learning Optimal Feedback Operators and their Polynomial Approximation
Karl Kunisch, Donato Vásquez-Varas, Daniel Walter
A learning based method for obtaining feedback laws for nonlinear optimal control problems is proposed. The learning problem is posed such that the open loop value function is its…
Exoplanet Characterization using Conditional Invertible Neural Networks
Jonas Haldemann, Victor Ksoll, Daniel Walter +6
The characterization of an exoplanet's interior is an inverse problem, which requires statistical methods such as Bayesian inference in order to be solved. Current methods employ M…
Extremal points of total generalized variation balls in 1D: characterization and applications
José A. Iglesias, Daniel Walter
The total generalized variation (TGV) is a popular regularizer in inverse problems and imaging combining discontinuous solutions and higher order smoothing. In particular, empirica…
Asymptotic linear convergence of fully-corrective generalized conditional gradient methods
Kristian Bredies, Marcello Carioni, Silvio Fanzon +1
We propose a fully-corrective generalized conditional gradient method (FC-GCG) for the minimization of the sum of a smooth, convex loss function and a convex one-homogeneous regula…
On fast convergence rates for generalized conditional gradient methods with backtracking stepsize
Karl Kunisch, Daniel Walter
A generalized conditional gradient method for minimizing the sum of two convex functions, one of them differentiable, is presented. This iterative method relies on two main ingredi…
A fast Primal-Dual-Active-Jump method for minimization in
Philip Trautmann, Daniel Walter
We analyze a solution method for minimization problems over a space of -valued functions of bounded variation on an interval . The presented method relies on piece…
Learning an optimal feedback operator semiglobally stabilizing semilinear parabolic equations
Karl Kunisch, Sérgio S. Rodrigues, Daniel Walter
Stabilizing feedback operators are presented which depend only on the orthogonal projection of the state onto the finite-dimensional control space. A class of monotone feedback ope…
Semiglobal optimal feedback stabilization of autonomous systems via deep neural network approximation
Karl Kunisch, Daniel Walter
A learning approach for optimal feedback gains for nonlinear continuous time control systems is proposed and analysed. The goal is to establish a rigorous framework for computing a…
A sparse control approach to optimal sensor placement in PDE-constrained parameter estimation problems
Ira Neitzel, Konstantin Pieper, Boris Vexler +1
We present a systematic approach to the optimal placement of finitely many sensors in order to infer a finite-dimensional parameter from point evaluations of the solution of an ass…
Numerical Analysis of Sparse Initial Data Identification for Parabolic Problems
Dmitriy Leykekhman, Boris Vexler, Daniel Walter
In this paper we consider a problem of initial data identification from the final time observation for homogeneous parabolic problems. It is well-known that such problems are expon…
Linear convergence of accelerated conditional gradient algorithms in spaces of measures
Konstantin Pieper, Daniel Walter
A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional…
Inverse point source location with the Helmholtz equation on a bounded domain
Konstantin Pieper, Bao Quoc Tang, Philip Trautmann +1
The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is a…