A bounded degree SOS hierarchy for large scale polynomial optimization with sparsity

Tillmann Weisser (1) , Jean-Bernard Lasserre (2, 1) , Kim-Chuan Toh (3)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 NUS - National University of Singapore

We provide a sparse version of the bounded degree SOS (BSOS) hierarchy for polynomial optimization problems. The presented version permits to handle large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies the running intersection property, this sparse BSOS hierarchy of semidefinite programs (with semidefinite constraints of fixed size) converges to the global optimum of the original problem. Moreover, for the class of SOS-convex problems, finite convergence takes place at the first step of the hierarchy, just as in the dense version.

Mots clés: Global Optimization; Semidefinite Programming; Sparsity; Large Scale Problems; Convex Relaxations; Positivity Certificates

Domaines: Optimisation et contrôle [math.OC]

Tillmann Weisser, Jean-Bernard Lasserre, Kim-Chuan Toh. A bounded degree SOS hierarchy for large scale polynomial optimization with sparsity . 2016. ⟨hal-01341931v1⟩