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We compute numerically the minimizers of the Dirichlet energy
among maps from the unit disc into the unit sphere that satisfy a boundary condition and a degree condition.
We use a Sobolev gradient algorithm for the minimization and we prove that its continuous version preserves the degree. For the discretization of the problem we use continuous P1 finite elements. We propose an original mesh-refining strategy needed to preserve the degree with the discrete version of the algorithm (which...
The construction of reduced order models for dynamical systems using
proper orthogonal decomposition (POD) is based on the information
contained in so-called snapshots. These provide the spatial
distribution of the dynamical system at discrete time instances.
This work is devoted to optimizing the choice of these time
instances in such a manner that the error between the POD-solution
and the trajectory of the dynamical system is minimized. First and
second order optimality systems are given. Numerical...
This paper is devoted to the numerical solution of stationary laminar Bingham fluids by path-following methods. By using duality theory, a system that characterizes the solution of the original problem is derived. Since this system is ill-posed, a family of regularized problems is obtained and the convergence of the regularized solutions to the original one is proved. For the update of the regularization parameter, a path-following method is investigated. Based on the differentiability properties...
This paper is devoted to the numerical solution of stationary
laminar Bingham fluids by path-following methods. By using duality theory, a
system that characterizes the solution of the original problem is derived.
Since this system is ill-posed, a family of regularized problems is obtained
and the convergence of the regularized solutions to the original one is proved.
For the update of the regularization parameter, a path-following method is
investigated. Based on the differentiability properties...
Control of quantum systems is central in a variety of present and perspective applications ranging from quantum optics and quantum chemistry to semiconductor nanostructures, including the emerging fields of quantum computation and quantum communication. In this paper, a review of recent developments in the field of optimal control of quantum systems is given with a focus on adjoint methods and their numerical implementation. In addition, the issues of exact controllability and optimal control are...
In this report we propose a new recursive matrix formulation of limited memory variable metric methods. This approach can be used for an arbitrary update from the Broyden class (and some other updates) and also for the approximation of both the Hessian matrix and its inverse. The new recursive formulation requires approximately multiplications and additions per iteration, so it is comparable with other efficient limited memory variable metric methods. Numerical experiments concerning Algorithm...
Semi–smooth Newton methods are analyzed for a class of variational inequalities in infinite dimensions. It is shown that they are equivalent to certain active set strategies. Global and local super-linear convergence are proved. To overcome the phenomenon of finite speed of propagation of discretized problems a penalty version is used as the basis for a continuation procedure to speed up convergence. The choice of the penalty parameter can be made on the basis of an estimate for the penalized...
Semi–smooth Newton methods are analyzed for a class of variational
inequalities in infinite dimensions.
It is shown that they are equivalent to certain active set strategies.
Global and local super-linear convergence are
proved. To overcome the phenomenon of finite speed of propagation of
discretized problems a penalty version
is used as the basis for a continuation procedure to speed up convergence.
The choice of the penalty parameter
can be made on the basis of an L∞ estimate
for the penalized...
In this paper sufficient second order optimality conditions for optimal control problems
subject to stationary variational inequalities of obstacle type are derived. Since
optimality conditions for such problems always involve measures as Lagrange multipliers,
which impede the use of efficient Newton type methods, a family of regularized problems is
introduced. Second order sufficient optimality conditions are derived for the regularized
problems...
In this paper sufficient second order optimality conditions for optimal control problems
subject to stationary variational inequalities of obstacle type are derived. Since
optimality conditions for such problems always involve measures as Lagrange multipliers,
which impede the use of efficient Newton type methods, a family of regularized problems is
introduced. Second order sufficient optimality conditions are derived for the regularized
problems...
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