Leírás
CCOR minikurzus
Időpontjai:
szeptember 7. (szerda) 10:00
szeptember 7. (szerda) 13:00
szeptember 8. (csütörtök) 9:30
Abstract:
The mini-course focuses on certain optimization problems on curved spaces. In the first part, I recall those geometric objects which are crucial in our investigations (basic elements from Riemannian and Finsler geometry, including geodesics, Jacobi fields, curvature, Busemann convexity, etc). In the second part I present the proximal point algorithm on Hadamard manifolds (i.e., on complete, simply connected Riemannian manifolds with nonpositive sectional curvature), emphasizing the role of the curvature constraint. I also mention from the literature some incorrect extensions of the proximal point algorithm on Hadamard manifolds arising from not well defined convexity notions. In addition, I present a variational approach to find Nash equilibria on Hadamard manifolds by using fine properties of the projection map; as a surprising byproduct, it turns out that Hadamard manifolds represent the optimal geometric framework for the theory of Nash equilibria. In the third part, I intend to present some elements from the optimal mass transport theory, - which have their roots in linear programming, - by providing simple proofs of the famous Brunn-Minkowski, Prékopa-Leindler and Borell-Brascamp-Lieb inequalities.
For Zoom access please contact E.-Nagy Marianna (marianna.eisenberg-nagy[at]uni-corvinus.hu).