Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Forschungsseminar Algorithmische Optimierung (AGs Hante/Walther)

Ort: Rudower Chaussee 25, Raum 2.417

Zeit: Donnerstag, 15:15 Uhr

Studierende und Gäste sind herzlich willkommen.

 

 

Vorträge im Wintersemester 2023/2024

 

 

   
27.11.2023

Verteidigung Masterarbeit Gloria Xiao

Beginn 12:00

Achtung: Geänderter Tag und Uhrzeit!

28.11.2023 Verteidigung Masterarbeit Arsen Hnatiuk
  Stochastic Aspects of Dynamical Low-Rank Approximation in the Context of Machine Learning
  Beginn: 13:15
  Achtung: Geänderter Tag und Uhrzeit!
   
30.11.2023 Sonja Steffensen, Institut für Geometrie und Praktische Mathematik, RWTH Aachen
 
On Multilevel Game Theory and its Applications 🖉

Hierarchical Nash game models are an important modelling tool in various applications to study a strategic non-cooperative decision process of individuals, where the individuals can be split into a hierarchy of at least two different groups. Such models are in general mathematically described by multilevel games.
In this talk we will give a short introduction into standard and in particular hierarchical game theory and present some important mathematical structures and properties of Single- and Multi-Leader-Follower Games. Moreover, we will have a look at suitable numerical methods for such games.
In the second part of the talk, we first study a discrete-dynamic multilevel game that is used to model the optimal control of a gas transmission network.The players of this game are given by the controller of the network, i.e. the so-called technical system operator (TSO) on the one hand and the users of the network, namely the gas buyers and sellers on the other hand. Here, we consider a fully dynamic version of the TSO’s optimal control problem using a coupled system of semi-linear isothermal Euler equations to describe the time dependent gas dynamics. We will analyse the original four-level problem, which can be reduced to a bilevel discrete-dynamic optimal control problem by means of the underlying potential game structure. Finally, we briefly present a dynamic Stackelberg game, i.e. a Single-Leader-Follower game, where the number of followers becomes (infinitely) large giving rise to a socalled Meanfield Stackelberg game.

   
14.12.2023 Gabriele Eichfelder, Fachgebiet Mathematische Methoden des Operations Research, TU Ilmenau
 
Multiobjective Mixed Integer Programming 🖉

Multiobjective mixed integer nonlinear optimization refers to mathematical programming problems where more than one nonlinear objective function needs to be optimized simultaneously and some of the variables are constrained to take integer values. In this talk, we give a short introduction to the basic concepts of multiobjective optimization. We give insights why the famous approach of scalarization might not be an appropriate method to solve these problems. Instead, we present two procedures to solve the problems directly. The first is a branch-and-bound method based on the use of properly defined lower bounds. We do not simply rely on convex relaxations, but we built linear outer approximations of the image set in an adaptive way. The second method is tailored for convex objective functions and is purely based on the criterion space. It uses ingredients from the well-known outer approximation algorithm from single-objective mixed-integer optimization and combines them with strategies to generate enclosures of nondominated sets by iteratively improving approximations. For both algorithms, we are able to guarantee correctness in terms of detecting the nondominated set of multiobjective mixed integer problems according to a prescribed precision.

   
18.01.2024 Bennet Gebken, Universität Paderborn

 

 

First- and second-order descent methods for nonsmooth optimization based on deterministic gradient sampling 🖉

In nonsmooth optimization, it is well known that the classical gradient is not a suitable object for describing the local behavior of a function. Instead, generalized derivatives from nonsmooth analysis, like the Clarke subdifferential, have to be employed. While in theory, the Clarke subdifferential inherits many useful properties from the classical gradient, there is a large discrepancy in practice: It is unstable, and for a general locally Lipschitz continuous function, it is impossible to compute. Thus, in practice, the Clarke subdifferential has to be approximated. A simple strategy to achieve this, known as gradient sampling, is based on approximating it by taking the convex hull of classical gradients evaluated at smooth points from a small neighborhood of a given point.
In this talk, I will present two descent methods for nonsmooth optimization that are based on this idea. However, in contrast to the standard gradient sampling approach, where the gradients are sampled randomly, both methods will be deterministic. I will begin with a first-order method, where new gradients are computed using a bisection subroutine. Afterwards, I will demonstrate how the gradient sampling methodology can be generalized to second-order derivates by sampling Hessian matrices in addition to gradients. This will lead to a second-order descent method that, at least in numerical experiments, shows a high speed of convergence.

   
01.02.2024 Moritz Link, Universität Konstanz
 
Multiobjective mixed-integer nonlinear
optimization with application to energy supply
networks 🖉

In light of the ongoing developments in the climate crisis, it is necessary to consider factors beyond the sole economic perspective in energy supply network planning. This gives rise to a classical multiobjective optimization problem in-
volving conflicting objective functions. The presence of choices in the model, coupled with the consideration of stationary flow equations, results in an optimization problem with a mixed-integer nonlinear structure. Following a short introduction of some model-specific details and arising challenges, we present a novel method for computing an enclosure of the nondominated set of such problems. We prove finite convergence and demonstrate its effectiveness through numerical experiments. We conclude by offering a preview of ongoing exten-
sions of this work.

   
08.02.2024 Vladimir Shikhman, TU Chemnitz
  TBA
   
22.02.2024

Verteidigung Masterarbeit Enrico Bergmann

Beginn 8:30

Achtung: Geänderter Tag und Uhrzeit!

   
22.02.2024

Verteidigung Masterarbeit Elisa Giesecke

Beginn 13:00

Achtung: Geänderter Tag und Uhrzeit!

   
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