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pro vyhledávání: '"Penalty Methods"'
Autor:
Cui, Cu, Kanschat, Guido
We present a matrix-free multigrid method for high-order discontinuous Galerkin (DG) finite element methods with GPU acceleration. A performance analysis is conducted, comparing various data and compute layouts. Smoother implementations are optimized
Externí odkaz:
http://arxiv.org/abs/2405.18982
We propose a deep learning algorithm for high dimensional optimal stopping problems. Our method is inspired by the penalty method for solving free boundary PDEs. Within our approach, the penalized PDE is approximated using the Deep BSDE framework pro
Externí odkaz:
http://arxiv.org/abs/2405.11392
Autor:
Fang, Rui
Penalty methods relax the incompressibility condition and uncouple velocity and pressure. Experience with them indicates that the velocity error is sensitive to the choice of penalty parameter $\epsilon$. So far, there is no effective \'a prior formu
Externí odkaz:
http://arxiv.org/abs/2404.11712
In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we study the l
Externí odkaz:
http://arxiv.org/abs/2309.01753
We study continuous data assimilation (CDA) applied to projection and penalty methods for the Navier-Stokes (NS) equations. Penalty and projection methods are more efficient than consistent NS discretizations, however are less accurate due to modelin
Externí odkaz:
http://arxiv.org/abs/2302.05962
Autor:
Lu, Zhaosong, Mei, Sanyou
In this paper we study a class of unconstrained and constrained bilevel optimization problems in which the lower level is a possibly nonsmooth convex optimization problem, while the upper level is a possibly nonconvex optimization problem. We introdu
Externí odkaz:
http://arxiv.org/abs/2301.01716
Akademický článek
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Autor:
Neuenhofen, Martin Peter
This thesis presents new mathematical algorithms for the numerical solution of a mathematical problem class called \emph{dynamic optimization problems}. These are mathematical optimization problems, i.e., problems in which numbers are sought that min
Externí odkaz:
http://arxiv.org/abs/2208.09264
Autor:
Layton, William, Xu, Shuxian
Penalizing incompressibility in the Stokes problem leads, under mild assumptions, to matrices with condition numbers $\kappa =\mathcal{O} (\varepsilon ^{-1}h^{-2})$, $\varepsilon =$ penalty parameter $<<1$, and $ h= $ mesh width $<1$. Although $\kapp
Externí odkaz:
http://arxiv.org/abs/2206.06971