A bio-inspired optimization tool, the Dynamic Monge-Kantorovich model. Numerical solutions and applications

Data Seminario: 
Ora Inizio: 
Ora Fine: 
Enrico Facca
Scuola Normale Superiore, Pisa

In this talk I will present the Dynamical Monge-Kantorovich model, a PDE system coupling an elliptic equation with a diffusion coefficient that change in time according to a non-linear dynamics.

The steady state of this system has been related to the different Optimal Transport problems, offering an efficient numerical scheme for their solution. We will explore some examples of application, like identification of the Cut-Locus of a point on manifold and the study of complex natural network.

The simplicity of the model allows simple but effective transformations of its core equations, that have been shown to be connected with different optimization problems, such as the Basis Pursuit Problem and the Shape Optimization Problem.