DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** Wujun Zhang, Rutgers University

**Title: ***
A rate of convergence of numerical optimal transport problem with quadratic cost
*

**Abstract:**
The goal in optimal transportation is to transport a measure mu(x)
into a measure nu(y) with minimal total effort with respect to a given
cost function c(x,y).
In recent years, optimal transport has many applications in evolutionary dynamics, statistics, and machine learning.
On way to approximate the optimal transport solution is to approximate
the measure mu by the convex combination of Dirac measure mu_h on
equally spaced nodal set and solve the discrete optimal transport
between mu_h and nu.
If the cost function is quadratic, i.e. c(x,y) = |x-y|^2, the optimal transport mapping is related to an important concept from computational geometry, namely Laguerre cells.
In this talk, we study the rate of convergence of the discrete optimal mapping using tools in computational geometry, such as Brunn-Minkowski inequality.
We show that the rate of convergence of the discrete mapping measured in W^1_1 norm is of order O(h^2) under suitable assumptions on the regularity of the optimal mapping.
We will also discuss the rate of convergence in the case that the optimal mapping is degenerate.

**Time:** Friday, April 19, 2019, 1:30-2:30pm

**Place:** Exploratory Hall, Room 4106

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491