##### Department of Mathematics,

University of California San Diego

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### Math 278C - Optimization and Data Science

## Kisun Lee

#### UCSD

## Polyhedral homotopy method for Nash equilibrium problem

##### Abstract:

In this talk, we discuss the problem of finding generalized Nash equilibria (GNE) in the viewpoint of sparse polynomials. To obtain optimality conditions for GNE, we consider the Karush-Kuhn-Tucker (KKT) system using the Lagrange multiplier. We discuss that if all objectives and constraints polynomials are generic, the number of solutions of the KKT system equals its mixed volume, and so the polyhedral homotopy method can be optimal for finding GNEs. Lastly, comparisons with existing methods will be given.

Host: Jiawang Nie

### November 3, 2021

### 3:00 PM

### Zoom Meeting ID: 991 9807 8858 Password: 278CFA21

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