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Tuesday, 20.02.2024, 10:15 (WIAS-ESH)
Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Martin Schmidt, Universität Trier:
A primer on bilevel optimization under uncertainty
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
As it is the case for “usual”, i.e., single-level, optimization problems, bilevel optimization problems can and most likely should be considered under uncertainty as well. In single-level optimization, uncertainty is due to noisy or incomplete data that defines the problem at hand. For bilevel optimization, the sources of uncertainty are richer. Besides data uncertainty, the two-player nature of these problems leads to cases in which (the observation of) the decision of the other player might be unknown to some extend - a setting that we call decision uncertainty and that cannot appear in single-level optimization.
In this talk, we give a brief overview over the young field of bilevel optimization under uncertainty and present a specific example for the modeling of decision uncertainty. Finally, we highlight the newly established connections between robust and bilevel optimization that might lead to a stronger connection of the two fields.
This talk is based on joint work with Yasmine Beck, Marc Goerigk, Jannis Kurtz, Ivana Ljubic, and Johannes Thürauf.

Host
WIAS Berlin
Tuesday, 20.02.2024, 14:00 (WIAS-ESH)
Seminar Interacting Random Systems
Jia-Jie Zhu, WIAS Berlin:
Kernelization, Approximation, and Entropy-Dissipation of Gradient Flows: from Wasserstein to Fisher-Rao
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
Motivated by various machine learning applications, we present a principled investigation of gradient flow dissipation geometry, emphasizing the Fisher--Rao-type gradient flows and the connections with Wasserstein space. Using the dynamic Benamou--Brenier formulation, we reveal a few precise connections between those flow dissipation geometries and commonly used machine learning tools such as Stein flows, kernel discrepancies, and nonparametric regression. In addition, we present analysis results in terms of Łojasiewicz type functional inequalities, with an explicit threshold condition for a family of entropy dissipation along the Fisher--Rao flows. Finally, we establish rigorous evolutionary $Gamma$-convergence for the Fisher--Rao type gradient flows obtained via regression, justifying the approximation beyond static pointwise convergence. Joint work with Alexander Mielke.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
Tuesday, 20.02.2024, 15:30 (WIAS-ESH)
Seminar Interacting Random Systems
Utkir Rozikov, Uzbekistan Institute of Mathematics:
Gibbs measures of Potts model on trees
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
The talk is devoted to Gibbs measures of the q-state Potts model on Cayley trees. We present recent results (since 2014) about all translation-invariant splitting Gibbs measures. In particular, some conditions on the parameters of the q-state Potts model will be given for the (non-) extremality of these measures in the set of all Gibbs measures.

Further Informations
Seminar Interacting Random Systems (Hybrid Event)

Host
WIAS Berlin
February 21, 2024 (WIAS-ESH)
Workshop/Konferenz: MATh.en.JEANS
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Wednesday, 21.02.2024, 14:00 (WIAS-Library)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Dr. Ioannis Papadopoulos, WIAS Berlin:
Computing multiple solutions of topology optimization problems
more ... Location
Weierstraß-Institut, Hausvogteiplatz 5-7, 10117 Berlin, R411

Abstract
Topology optimization finds the optimal material distribution of a fluid or solid in a domain, subject to PDE and volume constraints. The models often result in a PDE, volume and inequality constrained, nonconvex, infinite-dimensional optimization problem that may support many local minima. In practice, heuristics are used to obtain the global minimum, but these can fail even in the simplest of cases. In this talk, we will introduce the deflated barrier method, a second-order algorithm that solves such problems, has local superlinear convergence, and can systematically discover many of these local minima. We will present examples which include finding 42 solutions of the topology optimization of a fluid satisfying the Navier-Stokes equations and more recent work involving the three-dimensional topology optimization of a fluid in Stokes flow. Underpinning the algorithm is the deflation mechanism. Deflation prevents a Newton-like solver from converging to a solution that has already been discovered. Deflation is computationally cheap, it does not affect the conditioning of the discretized systems, it may be coupled with a finite difference, finite volume or finite element discretization, and it is easy to implement.

Further Informations
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations

Host
WIAS Berlin
Thursday, 22.02.2024, 10:00 (WIAS-405-406)
Software and Data Seminar
Marco Reidelbach; Silvia Polla:
MaRDMO: a tool for mathematical research data management
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Host
WIAS Berlin