52,902 research outputs found
Asymptotics of an optimal compliance-location problem
We consider the problem of placing n small balls of given radius in a certain
domain subject to a force f in order to minimize the compliance of the
configuration. Then we let n tend to infinity and look at the asymptotics of
the minimization problem, after properly scaling the functionals involved, and
to the limit distribution of the centres of the balls. This problem is both
linked to optimal location and shape optimization problems.Comment: 20 pages with 2 figures; final accepted version (minor changes, some
extra details on the positivity assumption on
Applying a phase field approach for shape optimization of a stationary Navier-Stokes flow
We apply a phase field approach for a general shape optimization problem of a
stationary Navier-Stokes flow. To be precise we add a multiple of the
Ginzburg--Landau energy as a regularization to the objective functional and
relax the non-permeability of the medium outside the fluid region. The
resulting diffuse interface problem can be shown to be well-posed and
optimality conditions are derived. We state suitable assumptions on the problem
in order to derive a sharp interface limit for the minimizers and the
optimality conditions. Additionally, we can derive a necessary optimality
system for the sharp interface problem by geometric variations without stating
additional regularity assumptions on the minimizing set
Quasi-concave density estimation
Maximum likelihood estimation of a log-concave probability density is
formulated as a convex optimization problem and shown to have an equivalent
dual formulation as a constrained maximum Shannon entropy problem. Closely
related maximum Renyi entropy estimators that impose weaker concavity
restrictions on the fitted density are also considered, notably a minimum
Hellinger discrepancy estimator that constrains the reciprocal of the
square-root of the density to be concave. A limiting form of these estimators
constrains solutions to the class of quasi-concave densities.Comment: Published in at http://dx.doi.org/10.1214/10-AOS814 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Numerical minimization of dirichlet laplacian eigenvalues of four-dimensional geometries
We develop the first numerical study in four dimensions of optimal eigenmodes associated with the Dirichlet Laplacian. We describe an extension of the method of fundamental solutions adapted to the four-dimensional context. Based on our numerical simulation and a postprocessing adapted to the identification of relevant symmetries, we provide and discuss the numerical description of the eighth first optimal domains.The work of the first author was partially supported by FCT, Portugal, through the program “Investigador FCT” with reference IF/00177/2013 and the scientific project PTDC/MATCAL/4334/2014.
The work of the second author was supported by the ANR, through the projects COMEDIC, PGMO, and OPTIFORMinfo:eu-repo/semantics/publishedVersio
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