• Citer

Convergent relaxations of polynomial optimization problems with non-commuting variables

par Pironio, Stefano ;Navascués, Miguel;Acín, Antonio
Référence SIAM journal on optimization, 20, 5, page (2157-2180)
Publication Publié, 2009

Article révisé par les pairs

• Détails
• Contenu

Résumé :

We consider optimization problems with polynomial inequality constraints in noncommuting variables. These noncommuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial inequalities as semidefinite positivity constraints. Such problems arise naturally in quantum theory and quantum information science. To solve them, we introduce a hierarchy of semidefinite programming relaxations which generates a monotone sequence of lower bounds that converges to the optimal solution. We also introduce a criterion to detect whether the global optimum is reached at a given relaxation step and show how to extract a global optimizer from the solution of the corresponding semidefinite programming problem. © 2010 Society for Industrial and Applied Mathematics.