Veranstaltungen
- Dienstag, 30.07.2024, 15:00 Uhr (WIAS-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Egor Gladin, Humboldt Universität zu Berlin:
Cutting plane methods and dual problems
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstrakt
The present talk examines cutting plane methods, which are a group of iterative algorithms for minimizing a (possibly nonsmooth) convex function over a compact convex set. We consider two prominent examples, namely, the ellipsoid method and Vaidya's method, and show that their convergence rate is preserved even when an inexact oracle is used. Furthermore, we demonstrate that it is possible to use these methods in the context of stochastic optimization efficiently. Another direction where cutting plane methods can be useful is Lagrange dual problems. Commonly, the objective and its derivatives can only be computed approximately in such problems. Thus, the methods' insensitivity to error in subgradients comes in handy. As an application example, we propose a linearly converging dual method for a constrained Markov decision process (CMDP) based on Vaidya's algorithm with an inexact oracle. The talk also discusses the concept of accuracy certificates for convex minimization problems. Certificates allow for online verification of the accuracy of approximate solutions and provide a theoretically valid online stopping criterion. We generalize the notion of accuracy certificates for the setting of an inexact first-order oracle. In particular, this includes the setting of a dual problem where the dual function and its derivatives don't necessarily have closed-form representations. Furthermore, we propose an explicit way to construct accuracy certificates for a large class of cutting plane methods that use polytopes as localizers.
Weitere Informationen
Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715
Veranstalter
WIAS Berlin
- Donnerstag, 08.08.2024, 13:30 Uhr (WIAS-406)
- Seminar Materialmodellierung
Dr. Ferran Brosa Planella, University of Warwick, GB:
Asymptotic methods for lithium-ion battery models
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Abstrakt
Lithium-ion batteries have become ubiquitous over the past decade, and they are called to play even a more important role with the electrification of vehicles. In order to design better and safer batteries and to manage them more efficiently, we need models than can predict the battery behaviour accurately and fast. However, in many cases these models are still posed in an ad hoc way, which makes them hard to extend and may lead to inconsistencies. In this talk we will see some examples on how asymptotic methods can be applied to obtain simple models that can be used in battery control and parameterisation.
Veranstalter
WIAS Berlin
- Donnerstag, 05.09.2024, 12:00 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Martijn Gösgens, TU Eindhoven, NL:
tba
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
tba
Weitere Informationen
Seminar Interacting Random Systems (Hybrid Event)
Veranstalter
WIAS Berlin
- Mittwoch, 18.09.2024, 10:00 Uhr (WIAS-405-406)
- Seminar Numerische Mathematik
Albert J. Pool, Deutsches Zentrum für Luft- und Raumfahrt e.V.:
Nonlinear dynamics as a ground-state solution on quantum computers
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
For the solution of time-dependent nonlinear differential equations, we present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution from a single ground-state computation. We describe a general procedure to construct efficient quantum circuits for the cost function evaluation required by VQAs. To mitigate the barren plateau problem during the optimization, we propose an adaptive multigrid strategy. The approach is illustrated for the nonlinear Burgers equation. We classically optimize quantum circuits to represent the desired ground-state solutions, run them on IBM Q System One and Quantinuum System Model H1, and demonstrate that current quantum computers are capable of accurately reproducing the exact results.
Veranstalter
WIAS Berlin
