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Robust \(\ell _1\) Approaches to Computing the Geometric Median and Principal and Independent Components

mathematical image processing with emphasis on MRI applications. Karl Kunisch is a professor and head of department of mathematics at the University of Graz, and Scientific Director of the Radon Institute of

Time optimal control of the heat equation with pointwise control constraints

ESAIM: COCV TIME OPTIMAL CONTROL OF THE HEAT EQUATION WITH POINTWISE CONTROL CONSTRAINTS Karl Kunisch 1 Lijuan 0 School of Mathematics and Statistics, Wuhan University , Wuhan 430072 , P.R. China 1

Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities

ESAIM: COCV 1. Introduction, problem statement, regularization Karl Kunisch 1 Daniel Wachsmuth 0 0 Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of

A duality-based approach to elliptic control problems in non-reflexive Banach spaces

Convex duality is a powerful framework for solving non-smooth optimal control problems. However, for problems set in non-reflexive Banach spaces such as L1(Ω) or BV(Ω), the dual problem is formulated in a space which has difficult measure theoretic structure. The predual problem, on the other hand, can be formulated in a Hilbert space and entails the minimization of a smooth...

The Output Least Squares Identifiability of the Diffusion Coefficient from an H1–Observation in a 2–D Elliptic Equation

Output least squares stability for the diffusion coefficient in an elliptic equation in dimension two is analyzed. This guarantees Lipschitz stability of the solution of the least squares formulation with respect to perturbations in the data independently of their attainability. The analysis shows the influence of the flow direction on the parameter to be estimated. A scale...