Convex optimization on polytopes arises in many areas of science. When the polytope is given implicitly or has exponentially many vertices and facets, standard methods may not apply or be ineffective. This is the case for moment polytopes, such as the entanglement polytopes, which play a foundational role in quantum information and algebraic complexity. They give rise to important entanglement measures and tensor parameters such as the quantum functionals, yet general effective methods for computing these quantities have been elusive. In this paper we address this challenge. We develop a first-order framework called Hadamard mirror descent to optimize suitable convex functions over moment polytopes and, more generally, the gradient sets of geodesically convex functions. It operates locally and does not rely on any explicit description of the polytope. Our framework extends mirror descent, an effective and widely used framework for convex optimization, from the Euclidean setting to Hadamard manifolds, and is motivated by a recent work by Hirai, which we interpret as a Hadamard version of mirror flow. Applying the framework to entanglement polytopes yields the first efficient first-order algorithms to compute the quantum functionals, the symmetric quantum functional, and the G-stable ranks, as well as a new direct algorithm for the non-commutative rank.

The shortest route problem is one of the most famous, well researched and real-world occurring problems in mathematics. Since the problem of finding the shortest route is one we often encounter daily, the significance of finding a fast and reliable algorithm to solve the problem is evident. While there exist many different algorithms today, the research for better algorithms is still noteworthy, as exemplified by new results circulating in the scientific world last year. In this talk I present uninformed and informed search algorithms, in particular the A*-Algorithm, used for solving shortest path problems for the situation of finding a shortest route in a real-world scenario. We will discuss whether using a bidirectional strategy can be an effective method for reducing runtime. An implementation of the considered algorithms, including a visual output, tested on different data sets will be shown. The difference between different kind of measures, notably the travel distance and the travel time, will play a part in the analysis. Lastly, the results will be evaluated and compared.

09:00-09:45 Niels Richard Hansen (University of Copenhagen)

09:45-10:30 Aad van der Vaart (TU Delft)

Coffee break

11:00-11:30 TUM-Speakers

11:30-12:15 Nadja Klein (Karlsruhe Institut of Technology)

Lunch break

13:45-14:15 TUM-Speakers

14:15-15:00 Mark Podolskij (University of Luxembourg)

Further information can be found here: https://collab.dvb.bayern/spaces/TUMmathstat/pages/2944080125/Miniworkshop+2026+Structure+and+ Uncertainty+in+Complex+Multivariate+Data