JeanBernard Lasserre CNRS 
Friday, June the 22nd
Moments and positivity certificates in and outside optimization
Abstract We first provide a brief description of the momentSOS (sumofsquares) hierarchy in global optimization which is based on powerful positivity certificates from real algebraic geometry. Combined with semidefinite programming it allows to define a hierarchy of convex relaxations. Each relaxation in the hierarchy is a semidefinite program whose size increases and the 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 for solving 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 applied mathematics, probability, statistics, computational geometry, control and optimal control.
