Thời gian: 15h00 (Giờ Việt Nam), thứ năm, ngày 24/3/2022.

Hình thức: Trực tuyến (link google meet: meet.google.com/zsh-jnxc-eit)

Abstract: In a first contribution, we revisit two certificates of positivity on (possibly non-compact) basic semialgebraic sets due to Putinar and Vasilescu (C R Acad Sci Ser I Math 328(6):495–499, 1999). We use Jacobi’s technique from (Math Z 237(2):259–273, 2001) to provide an alternative proof with an effective degree bound on the sums of squares weights in such certificates. As a consequence, it allows one to define a hierarchy of semidefinite relaxations for a general polynomial optimization problem. Convergence of this hierarchy to a neighborhood of the optimal value as well as strong duality and analysis are guaranteed. In a second contribution, we introduce a new numerical method for solving systems of polynomial inequalities and equalities with possibly uncountably many solutions. As a bonus, one can apply this method to obtain approximate global optimizers in polynomial optimization.

Joint work with: Jean-Bernard Lasserre and Victor Magron.