A tutorial on the Lasserre hierarchy in polynomial optimization and optimal control
Didier Henrion (LAAS-CNRS Univ. Toulouse et Czech Tech. Univ. Prague) donnera un séminaire jeudi 19 décembre à 10h dans la salle 124 jaune du CRAN à l'ENSEM.
Titre : A tutorial on the Lasserre hierarchy in polynomial optimization and optimal control.
Résumé : We survey a mathematical technology introduced in 2000 by Jean Bernard Lasserre to solve globally non-convex optimization problems on multivariate polynomials with the help of a hierarchy of convex semidefinite programming problems (linear matrix inequalities or LMI = linear programming problems in the cone of positive semidefinite matrices). Instrumental to the development of this technique is the duality between the cone of positive polynomials and the cone of moments, and the availability of sums of squares positivity certificates.
Then we apply this technology to polynomial optimal control problems, the minimization of a polynomial Lagrangian over a polynomial vector field subject to semi-algebraic control and state constraints, a nonconvex problem for which there is no solution in classical Lebesgue spaces. Joint work with Jean Bernard Lasserre, Edouard Pauwels, Christophe Prieur, Emmanuel Trélat, see arXiv:0703377 and also arXiv:1407.1650.
If time allows, we can explain how this approach could be applied as well to the optimal control of switching nonlinear systems. Joint work with Mathieu Claeys and Jamal Daafouz, see arXiv:1404.4699.