294 research outputs found
Limit points of the monotonic schemes
Many numerical simulations in quantum (bilinear) control use the
monotonically convergent algorithms of Krotov (introduced by Tannor), Zhu &
Rabitz or the general form of Maday & Turinici. This paper presents an analysis
of the limit set of controls provided by these algorithms and a proof of
convergence in a particular case.Comment: 5 pages, 0 figure, 44th IEEE conference on Decision and Control
Sevilla december 200
Local matching indicators for transport with concave costs
In this note, we introduce a class of indicators that enable to compute
efficiently optimal transport plans associated to arbitrary distributions of
demands and supplies in in the case where the cost
function is concave. The computational cost of these indicators is small and
independent of . A hierarchical use of them enables to obtain an efficient
algorithm
Parareal in time intermediate targets methods for optimal control problem
In this paper, we present a method that enables solving in parallel the
Euler-Lagrange system associated with the optimal control of a parabolic
equation. Our approach is based on an iterative update of a sequence of
intermediate targets that gives rise to independent sub-problems that can be
solved in parallel. This method can be coupled with the parareal in time
algorithm. Numerical experiments show the efficiency of our method.Comment: 14 page
Control through operators for quantum chemistry
We consider the problem of operator identification in quantum control. The
free Hamiltonian and the dipole moment are searched such that a given target
state is reached at a given time. A local existence result is obtained. As a
by-product, our works reveals necessary conditions on the laser field to make
the identification feasible. In the last part of this work, some algorithms are
proposed to compute effectively these operators
Reduced basis methods for pricing options with the Black-Scholes and Heston model
In this paper, we present a reduced basis method for pricing European and
American options based on the Black-Scholes and Heston model. To tackle each
model numerically, we formulate the problem in terms of a time dependent
variational equality or inequality. We apply a suitable reduced basis approach
for both types of options. The characteristic ingredients used in the method
are a combined POD-Greedy and Angle-Greedy procedure for the construction of
the primal and dual reduced spaces. Analytically, we prove the reproduction
property of the reduced scheme and derive a posteriori error estimators.
Numerical examples are provided, illustrating the approximation quality and
convergence of our approach for the different option pricing models. Also, we
investigate the reliability and effectivity of the error estimators.Comment: 25 pages, 27 figure
Control of Molecular orientation and alignement by monotonic schemes
International audienceMany numerical simulations in quantum (bilinear) control use monotonically convergent algorithms. A relevant time discretization has been proposed for these algorithms in [20]. We present here a way to apply these algorithms to the control of orientation and alignment. Numerical results that illustrate some of the properties of these algorithms are given
Optimal control of Nuclear Magnetic Resonance periodic systems
In this paper, we consider an optimal control problem for quantum systems with a periodic time evolution. In this non-classical problem both the initial and final state are unknown (and equal). We first prove the existence of periodic solution of this problem for a fixed period and study the associated optimal periodic control problem
A discrete-pulse optimal control algorithm with an application to spin systems
This article is aimed at extending the framework of optimal control
techniques to the situation where the control field values are restricted to a
finite set. We propose a generalization of the standard GRAPE algorithm suited
to this constraint. We test the validity and the efficiency of this approach
for the inversion of an inhomogeneous ensemble of spin systems with different
offset frequencies. It is shown that a remarkable efficiency can be achieved
even for a very limited number of discrete values. Some applications in Nuclear
Magnetic Resonance are discussed
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