31 citations · 72 across the 10 of their papers we have counts for
6 papers · 1 filter
A Bilevel Approach for Parameter Learning in Inverse Problems
Gernot Holler, Karl Kunisch, Richard C. Barnard
A learning approach to selecting regularization parameters in multi-penalty Tikhonov regularization is investigated. It leads to a bilevel optimization problem, where the lower lev…
A convex penalty for switching control of partial differential equations
Christian Clason, Armin Rund, Karl Kunisch +1
A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one…
L1 penalization of volumetric dose objectives in optimal control of PDEs
Richard C. Barnard, Christian Clason
This work is concerned with a class of optimal control problems governed by a partial differential equation that are motivated by an application in radiotherapy treatment planning,…
Flow Invariance on Stratified Domains
Richard Barnard, Peter Wolenski
This paper studies conditions for invariance of dynamical systems on stratified do- mains as originally introduced by Bressan and Hong. We establish Hamiltonian conditions for both…
State Constrained Optimization with Partial Differential Equations via Generalized Gradients
Richard Barnard
We consider optimization problems constrained by partial differential equations (PDEs) with additional constraints placed on the solution of the PDEs. We develop a general and vers…
Optimal radiotherapy treatment planning using minimum entropy models
Richard Barnard, Martin Frank, Michael Herty
We study the problem of finding an optimal radiotherapy treatment plan. A time-dependent Boltzmann particle transport model is used to model the interaction between radiative parti…