- Series
- Dissertation Defense
- Time
- Friday, April 12, 2024 - 1:30pm for 1.5 hours (actually 80 minutes)
- Location
- Skiles 268
- Speaker
- Daniyar Omarov – School of Mathematics, Georgia Tech – domarov3@gatech.edu
- Organizer
- Daniyar Omarov
I will present numerical methods for solving the optimal transport (OT) problems in three settings. Firstly, I will discuss discrete OT problems from the perspective of linear programming and assignment problems. Additionally, I will provide a solution for a discrete problem with an obstacle in the domain.
Next, I will consider and compare several different numerical methods to solve the classic continuous OT problem with the squared Euclidean cost function. I will compare two numerical methods used for the fluid dynamics formulation with a direct discretization of the Monge-Ampère PDE. Furthermore, I will introduce a new class of problems called separable, for which very accurate methods can be devised.
Lastly, I propose a novel implementation of Newton's method for solving semi-discrete OT problems for cost functions that are a positive combination of $p$-norms, $1