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Optimality Conditions for Bilevel Imaging Learning Problems with Total Variation Regularization
Juan Carlos De los Reyes, David Villacís
We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with total v…
An enriched second-order method for nonconvex composite sparse optimization problems
Pedro Merino, Juan Carlos De Los Reyes
In this paper we propose a second--order method for solving \emph{linear composite sparse optimization problems} consisting of minimizing the sum of a differentiable (possibly nonc…
A bilevel learning approach for optimal observation placement in variational data assimilation
Paula Castro, Juan Carlos De los Reyes
In this paper we propose a bilevel optimization approach for the placement of space and time observations in variational data assimilation problems. Within the framework of supervi…
Total Generalized Variation Regularization in Variational Data Assimilation for Burgers' Equation
J. C. De los Reyes, E. Loayza
We propose a second-order total generalized variation (TGV) regularization for the reconstruction of the initial condition in variational data assimilation problems. After showing…
On the optimal control of some nonsmooth distributed parameter systems arising in mechanics
Juan-Carlos De Los Reyes
Variational inequalities are an important mathematical tool for modelling free boundary problems that arise in different application areas. Due to the intricate nonsmooth structure…
A non-smooth trust-region method for locally Lipschitz functions with application to optimization problems constrained by variational inequalities
Constantin Christof, Juan Carlos De Los Reyes, Christian Meyer
We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational in…