77 citations · 625 across the 37 of their papers we have counts for
39 papers
Observability as a constraint qualification for a nonsmooth bilevel PDE-constrained problem
Christian Clason, Alberto Domínguez Corella, Jyrki Jauhiainen
Motivated by experiment design for parameter identification in image reconstruction, we analyze a bilevel control problem involving sparse inversion at the lower level. Qualified o…
Orlicz space relaxation of total variation denoising
Christian Clason, Tobias Unterberger
We consider variational image denoising with spatially dependent Orlicz regularization and introduce an Orlicz--Sobolev approximation of the ROF model based on a scaled -t…
Variational Analysis in Spectral Decomposition Systems
Hòa T. Bùi, Minh N. Bùi, Christian Clason
This work is concerned with the variational analysis of functions defined on Euclidean spaces whose values depend solely on certain invariants (``spectrum'') of their arguments, a…
Convex Analysis in Spectral Decomposition Systems
Hòa T. Bùi, Minh N. Bùi, Christian Clason
This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of…
Numerical analysis of a nonsmooth quasilinear elliptic control problem: II. Finite element discretization and error estimates
Christian Clason, Vu Huu Nhu, Arnd Rösch
In this paper, we carry out the numerical analysis of a nonsmooth quasilinear elliptic optimal control problem, where the coefficient in the divergence term of the corresponding st…
Numerical analysis of a nonsmooth quasilinear elliptic control problem: I. Explicit second-order optimality conditions
Christian Clason, Vu Huu Nhu, Arnd Rösch
In this paper, we derive explicit second-order necessary and sufficient optimality conditions of a local minimizer to an optimal control problem for a quasilinear second-order part…
Convex relaxation of discrete vector-valued optimization problems
Christian Clason, Carla Tameling, Benedikt Wirth
We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite s…
No-gap second-order optimality conditions for optimal control of a non-smooth quasilinear elliptic equation
Christian Clason, Vu Huu Nhu, Arnd Rösch
This paper deals with second-order optimality conditions for a quasilinear elliptic control problem with a nonlinear coefficient in the principal part that is countably (con…
Regularization of Inverse Problems
Christian Clason
These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framewor…
Introduction to Nonsmooth Analysis and Optimization
Christian Clason, Tuomo Valkonen
Functions that are not differentiable in the classical sense have become a central tool in modern mathematical models for imaging, inverse problems, machine learning, and optimal c…
Optimal control of the principal coefficient in a scalar wave equation
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. Adding a total variation penalty allows showing existence o…
Entropic regularization of continuous optimal transport problems
Christian Clason, Dirk A. Lorenz, Hinrich Mahler +1
We analyze continuous optimal transport problems in the so-called Kantorovich form, where we seek a transport plan between two marginals that are probability measures on compact su…
Bouligand-Levenberg-Marquardt iteration for a non-smooth ill-posed inverse problem
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 Gâteaux differentiable. By relaxing the…
Primal-dual proximal splitting and generalized conjugation in non-smooth non-convex optimization
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 w…
Optimal control of a non-smooth quasilinear elliptic equation
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 Lip…
Optimal control problems with control complementarity constraints
Christian Clason, Yu Deng, Patrick Mehlitz +1
A special class of optimal control problems with complementarity constraints on the control functions is studied. It is shown that such problems possess optimal solutions whenever…
Generalized modes in Bayesian inverse problems
Christian Clason, Tapio Helin, Remo Kretschmann +1
Uncertainty quantification requires efficient summarization of high- or even infinite-dimensional (i.e., non-parametric) distributions based on, e.g., suitable point estimates (mod…
Regularization of ill-posed problems with non-negative solutions
Christian Clason, Barbara Kaltenbacher, Elena Resmerita
This survey reviews variational and iterative methods for reconstructing non-negative solutions of ill-posed problems in infinite-dimensional spaces. We focus on two classes of met…
Quasi-solution of linear inverse problems in non-reflexive Banach spaces
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. Using the…
Error estimates for the approximation of multibang control problems
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 t…
Bouligand-Landweber iteration for a non-smooth ill-posed problem
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 Gâteaux differentiabl…
Contingent derivatives and regularization for noncoercive inverse problems
Christian Clason, Akhtar A. Khan, Miguel Sama +1
We study the inverse problem of parameter identification in non-coercive variational problems that commonly appear in applied models. We examine the differentiability of the set-va…
Acceleration and global convergence of a first-order primal--dual method for nonconvex problems
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 ari…
A Sinkhorn-Newton method for entropic optimal transport
Christoph Brauer, Christian Clason, Dirk Lorenz +1
We consider the entropic regularization of discretized optimal transport and propose to solve its optimality conditions via a logarithmic Newton iteration. We show a quadratic conv…