Zobrazeno 1 - 10
of 65
pro vyhledávání: '"Daniel Wachsmuth"'
Autor:
Eduardo Casas, Daniel Wachsmuth
Publikováno v:
SIAM Journal on Control and Optimization, 2023, 61(3), 1095-1112
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f97b8c16f6b18284a773cefd46f9092a
https://doi.org/10.1137/22m1486418
https://doi.org/10.1137/22m1486418
Autor:
Harbir Antil, Daniel Wachsmuth
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a0f93186606fea643cf52c67f8b5969e
http://arxiv.org/abs/2204.11456
http://arxiv.org/abs/2204.11456
Autor:
Daniel Wachsmuth, Nguyen Thanh Qui
Publikováno v:
SIAM Journal on Optimization. 30:1724-1755
The paper studies generalized differentiability properties of the marginal function of parametric optimal control problems of semilinear elliptic partial differential equations. We establish upper estimates for the regular and the limiting subgradien
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::05374a55893cc917e266e26dc4b37c9e
https://doi.org/10.1137/18m1200956
https://doi.org/10.1137/18m1200956
Autor:
Eduardo Casas, Daniel Wachsmuth
Publikováno v:
SIAM Journal on Control and Optimization, 2020, 58(6), 3486-3507
UCrea Repositorio Abierto de la Universidad de Cantabria
Universidad de Cantabria (UC)
UCrea Repositorio Abierto de la Universidad de Cantabria
Universidad de Cantabria (UC)
In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equation. The cost functional contains a term that measures the size of the support of the control, which is the so-called L0-norm. We provid
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2130803d55bb04fa0874d438f16fc838
https://doi.org/10.1137/20m1318377
https://doi.org/10.1137/20m1318377
Autor:
Daniel Wachsmuth
We investigate optimal control problems with $$L^0$$ L 0 constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation is us
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bdc74b059d1f4189f431f9f05d3ff97b
http://arxiv.org/abs/2201.05360
http://arxiv.org/abs/2201.05360
Publikováno v:
SIAM Journal on Optimization. 29:767-793
This paper deals with generalized Nash equilibrium problems (GNEPs) in Banach spaces. We give an existence result for normalized equilibria of jointly convex GNEPs and then propose an augmented Lag...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::afc20db5aaa903b3ea639ccd91b70e63
https://doi.org/10.1137/17m114114x
https://doi.org/10.1137/17m114114x
Autor:
Daniel Wachsmuth, Carolin Natemeyer
We investigate the convergence of the proximal gradient method applied to control problems with non-smooth and non-convex control cost. Here, we focus on control cost functionals that promote sparsity, which includes functionals of $$L^p$$ L p -type
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b714854a6b01eb8c98277f47bb981af5
https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/26906
https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/26906
In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the original pr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df81df8273aa02770b9cebf8a42646ab
https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-232811
https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-232811
Autor:
Nguyen Thanh Qui, Daniel Wachsmuth
Publikováno v:
Optimization. 67:2157-2177
In this paper, we investigate solution stability for control problems of partial differential equations with the cost functional not involving the usual quadratic term for the control. We first est...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ee774d02f544d7d8a42b0fe29a8b21c0
https://doi.org/10.1080/02331934.2018.1522634
https://doi.org/10.1080/02331934.2018.1522634
Autor:
Fredi Tröltzsch, Daniel Wachsmuth
Publikováno v:
Mathematical Control & Related Fields. 8:135-153
An optimal boundary control problem for the one-dimensional heat equation is considered. The objective functional includes a standard quadratic terminal observation, a Tikhonov regularization term with regularization parameter $ν$, and the $L^1$-nor
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::03e2817fdbd4055f383a832787ff445b
https://doi.org/10.3934/mcrf.2018006
https://doi.org/10.3934/mcrf.2018006