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pro vyhledávání: '"49j20"'
Autor:
Akiyama, Keito
In recent years, learning for neural networks can be viewed as optimization in the space of probability measures. To obtain the exponential convergence to the optimizer, the regularizing term based on Shannon entropy plays an important role. Even tho
Externí odkaz:
http://arxiv.org/abs/2411.03611
Autor:
Pfefferer, Johannes, Vexler, Boris
This paper is concerned with finite element error estimates for Neumann boundary control problems posed on convex and polyhedral domains. Different discretization concepts are considered and for each optimal discretization error estimates are establi
Externí odkaz:
http://arxiv.org/abs/2409.10736
In this paper, a reaction-diffusion system modeling injection of a chemotherapeutic drug on the surface of a living tissue during a treatment for cancer patients is studied. The system describes the interaction of the chemotherapeutic drug and the no
Externí odkaz:
http://arxiv.org/abs/2408.02227
Autor:
Gräßle, Carmen, Marquardt, Jannis
We interpret the 4D-var data assimilation problem for a parabolic partial differential equation (PDE) in the context of optimal control and revisit the process of deriving optimality conditions for an initial control problem. This is followed by a re
Externí odkaz:
http://arxiv.org/abs/2407.20866
Autor:
Liu, Sijing, Simoncini, Valeria
We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem constrained by a convection-dominated problem. We prove global optimal convergence rates using an inf-sup condition, with the diffusion parameter $\varepsi
Externí odkaz:
http://arxiv.org/abs/2406.09276
Autor:
Christof, Constantin
We study optimal control problems that are governed by semilinear elliptic partial differential equations that involve non-Lipschitzian nonlinearities. It is shown that, for a certain class of such PDEs, the solution map is Fr\'{e}chet differentiable
Externí odkaz:
http://arxiv.org/abs/2406.03110
We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal solutions,
Externí odkaz:
http://arxiv.org/abs/2405.05532
Stochastic optimization problems are generally known to be ill-conditioned to the form of the underlying uncertainty. A framework is introduced for optimal control problems with partial differential equations as constraints that is robust to inaccura
Externí odkaz:
http://arxiv.org/abs/2405.00176
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic distributed,
Externí odkaz:
http://arxiv.org/abs/2404.03756
Autor:
Schmidt, Niko
Publikováno v:
Nonlinear Analysis: Real World Applications, Volume 81, February 2025, 104197
The Antarctic and Greenland ice sheet simulation is challenging due to unknown parameters in the $p$-Stokes equations. In this work, we prove the existence of a solution to a parameter identification for the ice rheology and the friction coefficient.
Externí odkaz:
http://arxiv.org/abs/2404.01766