Veranstaltungen
- Dienstag, 23.04.2019, 14:00 Uhr (WIAS-406)
- Seminar Materialmodellierung
M. Milicevic, Albert-Ludwigs-Universität Freiburg:
The alternating direction method of multipliers with variable step sizes for the iterative solution of nonsmooth minimization problems and application to BV-damage evolution
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstrakt
The alternating direction method of multipliers (ADMM) is a flexible numerical method to solve a large class of convex minimization problems. Its most significant properties are the unconditional convergence with respect to the involved step size and the direct applicability. However, the performance critically depends on the choice of the step size. We propose an automated step size adjustment that relies on the monotonicity of the residual to accelerate the ADMM. Numerical experiments show a remarkable improvement over the standard ADMM with fixed step sizes. The ADMM with variable step sizes is then applied to a model for rate-independent, total variation regularized damage processes. The total variation regularization of the damage variable leads to sharp transitions of damaged to undamaged areas in the material. The results are compared to an H1-regularization of the damage and the simulations reveal that, indeed, for the total variation regularization sharp transitions can be observed whereas for the H1-regularization the interface is smeared out.
Veranstalter
WIAS Berlin
- Mittwoch, 24.04.2019, 10:00 Uhr (WIAS-ESH)
- Forschungsseminar Mathematische Statistik
Dr. Ch. Huang, Universität St. Gallen, Schweiz:
LASSO in time and space
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Abstrakt
We consider the estimation and inference in a system of high-dimensional regression equations allowing for temporal and cross-sectional dependency in covariates and error processes, covering rather general forms of weak dependence. A sequence of regressions with many regressors using LASSO (Least Absolute Shrinkage and Selection Operator) is applied for variable selection purpose, and an overall penalty level is carefully chosen by a block multiplier bootstrap procedure to account for multiplicity of the equations and dependencies in the data. Correspondingly, oracle properties with a jointly selected tuning parameter are derived. We further provide high-quality de-biased simultaneous inference on the many target parameters of the system. We provide bootstrap consistency results of the test procedure, which are based on a general Bahadur representation for the Z-estimators with dependent data. Simulations demonstrate good performance of the proposed inference procedure. Finally, we apply the method to quantify spillover effects of textual sentiment indices in a financial market and to test the connectedness among sectors.
Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
- Mittwoch, 24.04.2019, 15:15 Uhr (WIAS-ESH)
- Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. D. Peschka, WIAS Berlin:
Modeling, simulation, and experiments for flows of concentrated suspensions
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin