Séminaire de Probabilités
# Mini-course: Sum-of-squares optimization on finite sets (1/2)

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Salle F. Pellos, Room 207, Building 1R2 (IMT)
### Salle F. Pellos, Room 207, Building 1R2

#### IMT

Description

Title: Sum-of-squares optimization on finite sets

Abstract: If $X \subseteq R^n$ is a finite set then every function on

$X$ can be written as the restriction of a polynomial in n-variables. As

a result, polynomial optimization on finite sets is literally the same

as general (nonlinear) optimization on such sets. Thinking of functions

as polynomials however, provides us with plenty of additional structures

which can be leveraged for constructing better (or at least different)

optimization algorithms such as the sum-of-squares approach.

In this short course I will focus on explaining how sparsity, symmetry

and kernel methods can be leveraged for solving nonlinear optimization

problems on finite sets and will prove the recent definite results on

the hypercube due to Blekherman, Gouveia, Laurent, Nie, Parrilo,

Saunderson, Thomas and others.

The lectures will be a self-contained introduction to this very active

research area.

Times and locations:

- Monday 12th of june: 10:00 -> 12:00

Salle F. Pellos, Room 207, Building 1R2

- Tuesday 13th of june: 14:00 -> 16:00

Salle R. Huron, Room 106, Building 1R1

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