Jeudi 23 Mars

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Jeudi 23 Mars
Heure: 10:30 - 11:30
Lieu: Salle B107, bâtiment B, Université de Villetaneuse
Résumé: Exact algorithms for linear matrix inequalities and application to the moment problem
Description: Simone Naldi In this talk I will discuss computer algebra algorithms for solving exactly linear matrix inequalities, that is, the feasibility of a semidefinite program. These algorithms rely on the determinantal structure behind SDP. The main motivation is for certifying lower bounds in polynomial optimization, for instance, for computing the sum of squares certificates of multivariate polynomials. Recently a new application to the so-called truncated moment problem gives new perspectives that will be discussed in the second part of the talk. This consists of the decision problem whether a sequence of real numbers, indexed by monomials of degree d in n variables, is the moment sequence of a nonnegative Borel measure with support in some basic semialgebraic set. This is based on joint work with D. Henrion and M. Safey El Din.