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Regression has been successfully adapted to high-dimensional situations by penalization methods (review by Hesterberg, 2008), and penalized regression has been shown to outperform univariate and other multivariate regression methods in multiple genomic datasets (Bøvelstad et al., 2007).
Numerical issues involving local minima, mesh dependency, checkerboard patterns, and intermediate densities are tackled using continuation, filtering, and penalization methods.
We demonstrate that phase field methods are more accurate than penalization methods on problems with Neumann boundary conditions and we present an error analysis explaining this result.
Many problems in mathematical programming such as convex inclusion problems, minimax problems, penalization methods, goal programming problems, constrained optimization problems, and other problems can be formulated like composite optimization problems (see, for example, [1 6]).
In order to introduce solid obstacles into flows, several different methods are used, including volume penalization methods which prescribe appropriate boundary conditions by applying local forcing to the constitutive equations.
While it has been adapted for compressible, incompressible, viscous and inviscid flows, it is limited in the types of boundary conditions that it imposes, as are most volume penalization methods.
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The Brinkman penalization method was proposed for incompressible viscous flows by penalizing the momentum equations.
For the airborne launch problem a penalization method combined with the previous geometric analysis proves satisfying.
A volume penalization method for imposing homogeneous Neumann boundary conditions in advection diffusion equations is presented.
The SIMP (solid isotropic material with penalization) method is applied to optimize the distribution of foundation material.
The penalization method is used to take account of obstacles, such as the limiter, in a tokamak.
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