Z-mappings for mathematicians: Flavien Léger (INRIA Paris)Séminaire « Analyse numérique et équations aux dérivées partielles »
Z-mappings form a theory of non-variational problems initiated in the '70s but that has been for the most part overlooked by mathematicians.
In the first part of my talk I will show that although Z-mappings are not widely known, they can be found in a variety of contexts, such as:
- Hamilton-Jacobi-Bellman equations and their viscosity solutions,
- optimal transport,
- mean curvature flow,
- matching models in economics.
In the second part of the talk we will look at algorithms. Similar to how gradient descent is a natural algorithmic companion to convex problems, there exists a class of numerical methods naturally associated with Z-mappings. And it so happens that various well-established algorithms can be grouped under this point of view (Dijkstra's algorithm, MBO for interface dynamics, Bertsekas' naive auction, Sinkhorn, Gale-Shapley).