ESR9 - Lorenzo Baldi

Time is passing by, and work and study go ahead. In particular I am now studying different kind of boundary conditions that are necessary and/or sufficient to solve problems of constrained polynomial optimization. We are proving that different conditions present in the literature are more or less equivalent, and that under these hypothesis the moment relaxations enjoy good properties of convergence. I also planned with my supervisor four meetings/conferences between January and the end of April: of course the two POEMA ones, but also two more: la journée Moments  and Francophone Computer Algebra Days - Journées nationales de calcul formel : they will be busy, interesting months.

This is part of the POEMA Blogs that the ESRs of the project will maintain for the next three years. I started working at INRIA (Sophia Antipolis) in October. The research center is really a good place where to study: the team AROMATH, where I am hosted, is very international and there are often visitors from outside coming and giving talks, the offices are great (I will share mine with Tobias Christopher - ESR 10), and also the whether is good. I spent first weeks reading articles and discussing with my supervisor: the idea is to use techniques from commutative algebra, real algebraic geometry and moments to address questions in polynomial optimization. In particular now we are trying to prove (and improve) results from the sum of square relaxation to the moment relaxation.