Fiche de VU Trung-hieu

Titre : Certified Polynomial Optimization Based on Exact Sum of Squares Decompositions
Date : 9 décembre 2022
Heure: 09:00
Résumé : The aim of this thesis is to compute exact certificates of non-negativity for polynomials based on SOS decompositions with rational coefficients. We provide symbolic algorithms to compute SOS decompositions modulo the gradient ideal of non-negative real multivariate polynomials under a genericity condition. These algorithms can tackle a large range of problems which are out of reach for state-of-the-art algorithms. We also compute sums of Hermitian squares decompositions for complex trigonometric univariate polynomials that are positive on the unit circle with Gaussian coefficients. Moreover, we analyze the bit complexity of these algorithms and deduce bitsize bounds of such certificates. Finally, we implement these algorithms in the computer algebra system Maple and the programming environment Julia and evaluate their performance on some standard benchmarks.
Lieu : 4 Pl. Jussieu, 75005 Paris