39,216 research outputs found
Finite quantum tomography via semidefinite programming
Using the the convex semidefinite programming method and superoperator
formalism we obtain the finite quantum tomography of some mixed quantum states
such as: qudit tomography, N-qubit tomography, phase tomography and coherent
spin state tomography, where that obtained results are in agreement with those
of References \cite{schack,Pegg,Barnett,Buzek,Weigert}.Comment: 25 page
Multi-hadron states in Lattice QCD spectroscopy
The ability to reliably measure the energy of an excited hadron in Lattice
QCD simulations hinges on the accurate determination of all lower-lying
energies in the same symmetry channel. These include not only single-particle
energies, but also the energies of multi-hadron states. This talk deals with
the determination of multi-hadron energies in Lattice QCD. The
group-theoretical derivation of lattice interpolating operators that couple
optimally to multi-hadron states is described. We briefly discuss recent
algorithmic developments which allow for the efficient implementation of these
operators in software, and present numerical results from the Hadron Spectrum
Collaboration.Comment: 5 pages, 3 figures, talk given at Hadron 2009, Tallahassee, Florida,
December 1, 200
Accelerating two projection methods via perturbations with application to Intensity-Modulated Radiation Therapy
Constrained convex optimization problems arise naturally in many real-world
applications. One strategy to solve them in an approximate way is to translate
them into a sequence of convex feasibility problems via the recently developed
level set scheme and then solve each feasibility problem using projection
methods. However, if the problem is ill-conditioned, projection methods often
show zigzagging behavior and therefore converge slowly.
To address this issue, we exploit the bounded perturbation resilience of the
projection methods and introduce two new perturbations which avoid zigzagging
behavior. The first perturbation is in the spirit of -step methods and uses
gradient information from previous iterates. The second uses the approach of
surrogate constraint methods combined with relaxed, averaged projections.
We apply two different projection methods in the unperturbed version, as well
as the two perturbed versions, to linear feasibility problems along with
nonlinear optimization problems arising from intensity-modulated radiation
therapy (IMRT) treatment planning. We demonstrate that for all the considered
problems the perturbations can significantly accelerate the convergence of the
projection methods and hence the overall procedure of the level set scheme. For
the IMRT optimization problems the perturbed projection methods found an
approximate solution up to 4 times faster than the unperturbed methods while at
the same time achieving objective function values which were 0.5 to 5.1% lower.Comment: Accepted for publication in Applied Mathematics & Optimizatio
String-Averaging Projected Subgradient Methods for Constrained Minimization
We consider constrained minimization problems and propose to replace the
projection onto the entire feasible region, required in the Projected
Subgradient Method (PSM), by projections onto the individual sets whose
intersection forms the entire feasible region. Specifically, we propose to
perform such projections onto the individual sets in an algorithmic regime of a
feasibility-seeking iterative projection method. For this purpose we use the
recently developed family of Dynamic String-Averaging Projection (DSAP) methods
wherein iteration-index-dependent variable strings and variable weights are
permitted. This gives rise to an algorithmic scheme that generalizes, from the
algorithmic structural point of view, earlier work of Helou Neto and De Pierro,
of Nedi\'c, of Nurminski, and of Ram et al.Comment: Optimization Methods and Software, accepted for publicatio
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