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Tuesday, 20.02.2018, 15:00 (WIAS-406)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. P. Dvurechensky, WIAS Berlin:
Faster algorithms for (regularized) optimal transport
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
We propose an alternative to ubiquitous Sinkhorn algorithm for solving regularized optimal transport problem. Our approach is based on accelerated gradient descent applied to the dual problem and allows to solve not only entropy-regularized optimal transport problem, but also squared-2-norm-regularized OT problem, which produces sparser optimal transport plan approximation. We prove that, our algorithm, allows to solve non-regularized optimal transport problem with support size $p$ up to accuracy $epsilon$ in $Oleft(minleftfracp^9/4epsilon, fracp^2epsilon^2 rightright)$ arithmetic operations, which is better than state-of-the-art result $Oleft(fracp^2epsilon^3right)$.

Host
WIAS Berlin
Wednesday, 21.02.2018, 15:15 (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar) & Seminar Materialmodellierung
Dr. M. Morandotti, TU München:
Dimension reduction in the context of structured deformations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The theory of structured deformations shows good potential to deal with mechanical problems where multiple scales and fractures are present. Math- ematically, it amounts to relaxing a given energy functional and to show also the relaxed one has an integral representation. In this seminar, I will focus on a problem for thin objects: the derivation of a 2D relaxed energy via dimension reduction from a 3D energy, incorporat- ing structured deformations in the relaxation procedure. I will discuss the two-step relaxation (first dimension reduction, then structured deformations and vice versa) and I will compare it with another result in which the two relaxation procedures are carried out simultaneously. An explicit example for purely interfacial initial energies will complete the presentation. These results have been obtained in collaboration with G. Carita, J. Matias, and D.R. Owen.

Host
Humboldt-Universität zu Berlin
WIAS Berlin