Polynomial optimization, LMI and dynamical systems

Résumé

The first part of the talk surveys achievements of the last decade on polynomial optimisation and semidefinite programming (linear matrix inequalities, LMI) with a focus on the generalised problem of moments and existing software tools. The second part of the talk deals with a recent extension of these techniques to differential equations, dynamical systems and optimal control (primal problem on occupation measures, dual problem on viscosity solutions of Hamilton-Jacobi-Bellman partial differential equations).