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Kolloquium der Arbeitsgruppe Modellierung • Numerik • Differentialgleichungen

Sommersemester 201616
Verantwortliche Dozenten:
Alle Professoren der
Arbeitsgruppe Modellierung • Numerik • Differentialgleichungen
Koordination:
Dr. Christian Schröder, Dr. Hans-Christian Kreusler
Termine:
Di 16-18 Uhr in MA 313 und nach Vereinbarung
Inhalt:
Vorträge von Gästen und Mitarbeitern zu aktuellen Forschungsthemen

Beschreibung

Das Kolloquium der Arbeitsgruppe "Modellierung, Numerik, Differentialgleichungen" im Institut der Mathematik ist ein Kolloquium klassischer Art. Es wird also von einem breiten Kreis der Professoren und Mitarbeiter aus allen zugehörigen Lehrstühlen, insbesondere Angewandte Funktionalanalysis, Numerische Lineare Algebra, und Partielle Differentialgleichungen, besucht. Auch Studierende nach dem Bachelorabschluss zählen schon zu den Teilnehmern unseres Kolloquiums.

Aus diesen Gründen freuen wir uns insbesondere über Vorträge, die auf einen nicht spezialisierten Hörerkreis zugeschnitten sind und auch von Studierenden nach dem Bachelorabschuss bereits mit Profit gehört werden können.

Terminplanung / schedule
Datum
date
Zeit
time
Raum
room
Vortragende(r)
speaker
Titel
title
Einladender
invited by
3.05.16
16:15
MA 313
Thorsten Raasch
(U Mainz)
Global convergence of generalized Newton methods in nonsmooth optimization (Abstract)
G. Kutyniok
10.05.16
16:15
MA 313
Alberto Valli
(U Trento)
Finite elements in electromagnetism and application to eddy current equations (Abstract)
F. Tröltzsch
17.05.16
16:15
MA 313
Martin Schmidt
(U Erlangen-Nürnberg)
Mixed-Integer Nonlinear Optimization of Stationary Gas Transport Problems (Abstract)
V. Mehrmann
24.05.16
16:15
MA 313
Michal Wojtylak
(Jagiellonian U Krakow)
Rank two perturbations of operators and matrices (Abstract)
V. Mehrmann
31.05.16
16:15
MA 313
Pierre Weiss
(U Toulouse)
Compressed sensing with structured acquisition (Abstract)
G. Kutyniok
18.10.16
16:15
MA 313
Jose-Antonio Carrillo
(Imperial College London)
to be announced
V. Mehrmann

Abstracts zu den Vorträgen:

Thorsten Raasch (U Mainz)

Global convergence of generalized Newton methods in nonsmooth optimization
Dienstag, den 3.05.2016, 16.15 Uhr in MA 313
Abstract

We are concerned with the design of robust numerical methods for optimization problems with nonsmooth objective functions and/or nonsmooth constraints, like those arising from l1 or nuclear norm regularization. In these cases, the associated first-order optimality conditions have an equivalent reformulation as a piecewise smooth system of equations and can in turn be solved by generalized Newton methods. Such schemes have the advantage of locally superlinear or even locally quadratic convergence, and they often permit globalization by exact or inexact line search with respect to a suitable merit functional. Generalized Newton methods have been proposed and investigated since the late 1980s in the context of optimal control with smooth cost functionals and inequality control constraints, both in a finite- and infinite-dimensional setting. However, the analysis of globally convergent generalized Newton methods for nonsmooth regularization problems could be addressed only recently. This is mainly due to the fact that the optimality conditions of l1-regularization problems, e.g., are structurally different from those corresponding to smooth optimal control problems.

In this talk, we review the history of generalized Newton methods, and we discuss the design of semismooth and Bouligand-semismooth Newton schemes for l1-regularized recovery problems. Global convergence of the iteration is achieved by inexact line search with respect to the residual norm of the first-order optimality conditions. Various numerical examples are presented, ranging form image processing applications to parameter identification problems for PDEs. We discuss how to incorporate nonsmooth constraints and how to apply generalized Newton schemes to nuclear norm regularization problems.

The talk is based on joint work with Esther Hans (JGU Mainz), Dirk Lorenz (TU Braunschweig) and Christian Clason (U Duisburg-Essen).

Preceding this talk there will be coffee, tea, and biscuits at 15:45 in room MA 315 - everybody's welcome.

Alberto Valli (U Trento)

Finite elements in electromagnetism and application to eddy current equations
Dienstag, den 10.05.2016, 16.15 Uhr in MA 313
Abstract

One of the most successful methods used in numerical approximation of partial differential equations is without a doubt the finite element method. In this talk we first present which type of finite elements are employed in electromagnetism, and in which way the associated degrees of freedom are chosen. Then we briefly describe how the numerical approximation of Maxwell equations stems from the variational formulation of the problem. Finally, the eddy current approximation of Maxwell equations is introduced, and it is shown how topological concepts enter into play when looking for an efficient numerical solution of this problem.

Preceding this talk there will be coffee, tea, and biscuits at 15:45 in room MA 315 - everybody's welcome.

Martin Schmidt (U Erlangen-Nürnberg)

Mixed-Integer Nonlinear Optimization of Stationary Gas Transport Problems
Dienstag, den 17.05.2016, 16.15 Uhr in MA 313
Abstract

Modeling, simulation, and optimization of gas transport through pipeline systems is currently a highly active field of research. Due to highly nonlinear models of gas physics and engineering as well as discrete-continuous models of controllable network devices, the optimization of pipeline system operation and planning leads to large-scale mixed-integer nonlinear and nonconvex optimization or feasibility problems.

In this talk we discuss a two-stage solution approach for the feasibility problems. The first stage decides on the discrete controls of all active network devices with respect to a coarse approximation of physics and the second stage afterwards validates these controls with respect to detailed gas physics and engineering models. The first stage still is a nonconvex MINLP that we solve using a tailored MIP-based penalty alternating direction method whereas the second stage is a purely continuous NLP that we solve using a sequential approach.

Algorithmic aspects of both stages are discussed and numerical results on large-scale real-world networks show the applicability of the approach.

Preceding this talk there will be coffee, tea, and biscuits at 15:45 in room MA 315 - everybody's welcome.

Michal Wojtylak (Jagiellonian U Krakow)

Rank two perturbations of operators and matrices
Dienstag, den 24.05.2016, 16.15 Uhr in MA 313
Abstract

The rank one perturbations have gained recently much attention. In its simplest version, the problem can be formulated as follows. Suppose that A is a matrix with some given spectrum and Jordan structure. What is then the spectrum of a rank one perturbation A+uv^*?

The problem may be considered in many variations. Frequently it is assumed that the matrix A has a special structure of entries (e.g. real symmetric matrix or Hamiltonian matrix) or one may consider a linear pencils A+zE. Another step forward is to consider rank two perturbations.

The motivation for this research comes from many sources. For example, in numerical analysis many backward errors are modeled with rank one matrices. Furthermore, when modeling an electrical RCL circuit we get linear pencil with a special structure of entries. Changing one parameter of the circuit (e.g. one of the resistors, capacitors or inductors) leads usually to rank two perturbations of the pencil.

In the talk beside elaborating on the motivations we will discuss current results on rank two perturbations of matrices and operators (joint work with A. Kula and J. Wysoczanski, Wroclaw University), paying some attention to problems appearing in the infinite dimensional setting.

Preceding this talk there will be coffee, tea, and biscuits at 15:45 in room MA 315 - everybody's welcome.

Pierre Weiss (U Toulouse)

Compressed sensing with structured acquisition
Dienstag, den 31.05.2016, 16.15 Uhr in MA 313
Abstract

How to optimally design a sampling pattern given a set of acquisition constraints? This question is mostly unsolved, despite being essential for many applications such as Magnetic Resonance Imaging, X-ray and electron tomography, surface scattering,...

In this talk, I will provide an overview of recent results that I obtained with my collaborators in an attempt to better understand this problem and provide practical solutions for the Iseult project: the largest MRI system in the world. From a theoretical point of view, our study yields a new perspective on the theory of compressed sensing. From a numerical point of view, it opens new challenges on the optimization over spaces of measures.

Preceding this talk there will be coffee, tea, and biscuits at 15:45 in room MA 315 - everybody's welcome.

Zusatzinformationen / Extras