Zobrazeno 1 - 10
of 191
pro vyhledávání: '"Wachsmuth, Daniel"'
Autor:
Wachsmuth, Daniel
We consider nonsmooth optimal control problems subject to a linear elliptic partial differential equation with homogeneous Dirichlet boundary conditions. It is well-known that local solutions satisfy the celebrated Pontryagin maximum principle. In th
Externí odkaz:
http://arxiv.org/abs/2406.19010
Autor:
Wachsmuth, Daniel
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In contrast to ea
Externí odkaz:
http://arxiv.org/abs/2405.04204
Autor:
Dittrich, Bastian, Wachsmuth, Daniel
We consider constraints on the measure of the support for integrable functions on arbitrary measure spaces. It is shown that this non-convex and discontinuous constraint can be equivalently reformulated by the difference of two convex and continuous
Externí odkaz:
http://arxiv.org/abs/2403.19437
Autor:
Lentz, Anna, Wachsmuth, Daniel
We investigate time-dependent optimization problems in fractional Sobolev spaces with the sparsity promoting $L^p$-pseudo norm for $0
Externí odkaz:
http://arxiv.org/abs/2402.14417
Motivated by the residual type neural networks (ResNet), this paper studies optimal control problems constrained by a non-smooth integral equation. Such non-smooth equations, for instance, arise in the continuous representation of fractional deep neu
Externí odkaz:
http://arxiv.org/abs/2302.05318
Publikováno v:
Inverse Problems 40:015013 (2024)
Testing of hypotheses is a well studied topic in mathematical statistics. Recently, this issue has also been addressed in the context of Inverse Problems, where the quantity of interest is not directly accessible but only after the inversion of a (po
Externí odkaz:
http://arxiv.org/abs/2212.12897
Autor:
Wachsmuth, Daniel
Publikováno v:
Journal of Nonsmooth Analysis and Optimization, Volume 5, Original research articles (June 26, 2024) jnsao:12366
In this paper, we consider optimization problems with $L^0$-cost of the controls. Here, we take the support of the control as independent optimization variable. Topological derivatives of the corresponding value function with respect to variations of
Externí odkaz:
http://arxiv.org/abs/2211.12246
Autor:
Antil, Harbir, Wachsmuth, Daniel
Publikováno v:
Inverse problems 39, 044001 (2023)
We consider optimization problems in the fractional order Sobolev spaces $H^s(\Omega)$, $s\in (0,1)$, with sparsity promoting objective functionals containing $L^p$-pseudonorms, $p\in (0,1)$. Existence of solutions is proven. By means of a smoothing
Externí odkaz:
http://arxiv.org/abs/2204.11456
Autor:
Wachsmuth, Daniel, Wachsmuth, Gerd
We give a simple proof of the Baillon-Haddad theorem for convex functions defined on open and convex subsets of Hilbert spaces. We also state some generalizations and limitations. In particular, we discuss equivalent characterizations of the Lipschit
Externí odkaz:
http://arxiv.org/abs/2204.00282
Autor:
Casas, Eduardo, Wachsmuth, Daniel
In this paper, we study optimal control problems of semilinear elliptic and parabolic equations. A tracking cost functional, quadratic in the control and state variables, is considered. No control constraints are imposed. We prove that the correspond
Externí odkaz:
http://arxiv.org/abs/2203.12996