no code implementations • 2 Jan 2020 • Christian Clason
These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces.
Functional Analysis Numerical Analysis Numerical Analysis
1 code implementation • 18 Dec 2019 • Christian Clason, Karl Kunisch, Philip Trautmann
We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part.
Optimization and Control
1 code implementation • 27 Feb 2019 • Christian Clason, Vu Huu Nhu
In this paper, we consider a modified Levenberg--Marquardt method for solving an ill-posed inverse problem where the forward mapping is not G\^ateaux differentiable.
Numerical Analysis Optimization and Control
1 code implementation • 9 Jan 2019 • Christian Clason, Stanislav Mazurenko, Tuomo Valkonen
We demonstrate that difficult non-convex non-smooth optimization problems, such as Nash equilibrium problems and anisotropic as well as isotropic Potts segmentation model, can be written in terms of generalized conjugates of convex functionals.
Optimization and Control
1 code implementation • 18 Oct 2018 • Christian Clason, Vu Huu Nhu, Arnd Rösch
This work is concerned with an optimal control problem governed by a non-smooth quasilinear elliptic equation with a nonlinear coefficient in the principal part that is locally Lipschitz continuous and directionally but not G\^ateaux differentiable.
Optimization and Control
no code implementations • 27 Mar 2018 • Christian Clason, Andrej Klassen
We consider the method of quasi-solutions (also referred to as Ivanov regularization) for the regularization of linear ill-posed problems in non-reflexive Banach spaces.
Optimization and Control Numerical Analysis
1 code implementation • 12 Mar 2018 • Christian Clason, Thi Bich Tram Do, Frank Pörner
This work is concerned with optimal control problems where the objective functional consists of a tracking-type functional and an additional "multibang" regularization functional that promotes optimal control taking values from a given discrete set pointwise almost everywhere.
Optimization and Control Numerical Analysis
1 code implementation • 6 Mar 2018 • Christian Clason, Vu Huu Nhu
This work is concerned with the iterative regularization of a non-smooth nonlinear ill-posed problem where the forward mapping is merely directionally but not G\^ateaux differentiable.
Numerical Analysis Optimization and Control
no code implementations • 9 Feb 2018 • Christian Clason, Stanislav Mazurenko, Tuomo Valkonen
The primal--dual hybrid gradient method (PDHGM, also known as the Chambolle--Pock method) has proved very successful for convex optimization problems involving linear operators arising in image processing and inverse problems.
Optimization and Control
1 code implementation • 18 Oct 2017 • Christoph Brauer, Christian Clason, Dirk Lorenz, Benedikt Wirth
We further investigate numerically the robustness of the proposed method with respect to parameters such as the mesh size of the discretization.
no code implementations • 21 Aug 2017 • Christian Clason, Florian Kruse, Karl Kunisch
This work is concerned with the determination of the diffusion coefficient from distributed data of the state.
Optimization and Control
1 code implementation • 4 Jul 2017 • Christian Clason, Thi Bich Tram Do
This work is concerned with linear inverse problems where a distributed parameter is known a priori to only take on values from a given discrete set.
Optimization and Control
1 code implementation • 24 Feb 2017 • Christian Clason, Karl Kunisch
This work is concerned with optimal control of partial differential equations where the control enters the state equation as a coefficient and should take on values only from a given discrete set of values corresponding to available materials.
Optimization and Control
1 code implementation • 24 Feb 2017 • Christian Clason, Anton Schiela
Optimal control problems without control costs in general do not possess solutions due to the lack of coercivity.
Optimization and Control
1 code implementation • 24 Feb 2017 • Christian Clason, Kazufumi Ito, Karl Kunisch
Optimal control problems involving hybrid binary-continuous control costs are challenging due to their lack of convexity and weak lower semicontinuity.
Optimization and Control
1 code implementation • 24 Feb 2017 • Christoph Aigner, Christian Clason, Armin Rund, Rudolf Stollberger
RF pulse design via optimal control is typically based on gradient and quasi-Newton approaches and therefore suffers from slow convergence.
Optimization and Control
1 code implementation • 24 Feb 2017 • Christian Clason, Armin Rund, Karl Kunisch, Richard C. Barnard
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 should be simultaneously active.
Optimization and Control
1 code implementation • 23 Nov 2016 • Christian Clason, Carla Tameling, Benedikt Wirth
We consider a class of (ill-posed) optimal control problems in which a distributed vector-valued control is enforced to pointwise take values in a finite set $\mathcal{M}\subset\mathbb{R}^m$.
Optimization and Control
1 code implementation • 6 Jul 2016 • Richard C. Barnard, Christian Clason
The performance of this method for a model problem is illustrated and contrasted with the alternative approach based on (regularized) state constraints.
Optimization and Control
1 code implementation • 20 Jun 2016 • Christian Clason, Tuomo Valkonen
We study the extension of the Chambolle--Pock primal-dual algorithm to nonsmooth optimization problems involving nonlinear operators between function spaces.
Optimization and Control
1 code implementation • 31 May 2016 • Christian Clason, Armin Rund, Karl Kunisch
This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control.
Optimization and Control
