##### Department of Mathematics,

University of California San Diego

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### Math 278B (mathematics of information, data, and signals)

## Jun Kitagawa

#### Michigan State University

## Optimal transport with storage fees: theory and numerics

##### Abstract:

In this talk I will discuss the optimal transport problem with ``storage fees.'' This is a variant of the semi-discrete optimal transport (a.k.a. Monge-Kantorovich) problem, where instead of transporting an absolutely continuous measure to a fixed discrete measure and minimizing the transport cost, one must choose the weights of the target measure, and minimize the sum of the transport cost and some given ``storage fee function'' of the target weights. This problem arises in queue penalization and semi-supervised data clustering. I will discuss some basic theoretical questions, such as existence, uniqueness, a dual problem, and characterization of solutions. Then, I will present a numerical algorithm which has global linear and local superlinear convergence for a subcase of storage fee functions. \\ \\ All work in this talk is joint with M. Bansil (UCLA).

Host: Rayan Saab

### October 8, 2020

### 11:30 AM

### https://msu.zoom.us/j/96421373881 (Password: first prime number greater than 100)

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