Positivity certificates and polynomial optimization on non-compact semialgebraic sets - LAAS - Laboratoire d'Analyse et d'Architecture des Systèmes Accéder directement au contenu
Article Dans Une Revue Mathematical Programming, Series A Année : 2021

Positivity certificates and polynomial optimization on non-compact semialgebraic sets

Résumé

In a first contribution, we revisit two certificates of positivity on (possibly non-compact) basic semialgebraic sets due to Putinar and Vasilescu [Comptes Rendus de l'Acad\'emie des Sciences-Series I-Mathematics, 328(6) (1999) pp. 495-499]. We use Jacobi's technique from [Mathematische Zeitschrift, 237(2) (2001) pp. 259-273] to provide an alternative proof with an effective degree bound on the sums of squares multipliers 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 may apply this method to obtain approximate global optimizers in polynomial optimization.

Dates et versions

hal-02382059 , version 1 (27-11-2019)

Identifiants

Citer

Ngoc Hoang Anh Mai, Jean-Bernard Lasserre, Victor Magron. Positivity certificates and polynomial optimization on non-compact semialgebraic sets. Mathematical Programming, Series A, 2021, ⟨10.1007/s10107-021-01634-1⟩. ⟨hal-02382059⟩
79 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More