Colloquium de l'Institut

Sums of Squares: from Algebra to Analysis

by Francis Bach

Amphi Schwartz (Institut de Mathématiques de Toulouse, bâtiment 1R3)

Amphi Schwartz

Institut de Mathématiques de Toulouse, bâtiment 1R3

118, route de Narbonne F-31062 Toulouse Cedex 9

The representation of non-negative functions as sums of squares has become
an important tool in many modeling and optimization tasks. Traditionally
applied to polynomial functions, it requires rich tools from algebraic
geometry that led to many developments in the last twenty years. In this
lecture, I will look at this problem from a functional analysis point of
view, leading to new applications and new results on the performance of
sum-of-squares optimization.