Jean-Bernard Lasserre, French National Centre for Scientific Research

Abstract

We first provide a brief description of the "moment-SOS hierarchy". Initially designed for solving polynomial optimization problems, it is based on powerful positivity certificates from real algebraic geometry combined with semidefinite programming (an efficient technique from convex optimization).  it consists of a hierarchy of convex (semidefinite) relaxations whose size increases and whose associated monotone sequence of optimal values converges to the global minimum. Finite convergence is generic and fast in practice. 

In fact, this methodology also applies to solve the "Generalized Problem of Moments" (GPM) (of which global optimization is only a particular instance, and even the simplest). Then we briefly describe its application to several of many other applications outside optimization, notably in dynamical systems (control, optimal control, and analysis of some non-linear hyperbolic PDEs), statistics (optimal design), probability, computational geometry?