arXiv subjects

Carolin Natemeyer

Publications and source records attributed to Carolin Natemeyer.

2 recordsLinked to original sources

arXiv2021

A penalty scheme to solve constrained non-convex optimization problems in $BV(Ω)$

We investigate non-convex optimization problems in $BV(Ω)$ with two-sided pointwise inequality constraints. We propose a regularization and penalization method to numerically solve the problem. Under certain conditions, weak limit points of iterates are stationary for the original problem. In addition, we prove optimality conditions for the original problem that contain Lagrange multipliers to the inequality constraints. Numerical experiments confirm the theoretical findings.

math.OC↗

arXiv2020

A proximal gradient method for control problems with nonsmooth and nonconvex control cost

We investigate the convergence of an application of a proximal gradient method to control problems with nonsmooth and nonconvex control cost. Here, we focus on control cost functionals that promote sparsity, which includes functionals of $L^p$-type for $p\in [0,1)$. We prove stationarity properties of weak limit points of the method. These properties are weaker than those provided by Pontryagin's maximum principle and weaker than $L$-stationarity.

math.OC↗