Compact relaxations for polynomial programming problems

Sonia Cafieri (1) , Pierre Hansen (2, 3) , Lucas Létocart (4) , Leo Liberti (3) , Frédéric Messine (5, 6)

1 MAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l'Aérien
2 HEC Montréal - HEC Montréal
3 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
4 LIPN - Laboratoire d'Informatique de Paris-Nord
5 ENSEEIHT - Ecole Nationale Supérieure d'Electrotechnique, d'Electronique, d'Informatique, d'Hydraulique et de Télécommunications
6 IRIT-APO - Algorithmes Parallèles et Optimisation

Reduced RLT constraints are a special class of Reformulation- Linearization Technique (RLT) constraints. They apply to nonconvex (both continuous and mixed-integer) quadratic programming problems subject to systems of linear equality constraints. We present an extension to the general case of polynomial programming problems and discuss the derived convex relaxation. We then show how to perform rRLT constraint generation so as to reduce the number of inequality constraints in the relaxation, thereby making it more compact and faster to solve. We present some computational results validating our approach.

Mots clés: polynomial; nonconvex; MINLP; sBB; reformulation; convex relaxation; RLT

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Sonia Cafieri, Pierre Hansen, Lucas Létocart, Leo Liberti, Frédéric Messine. Compact relaxations for polynomial programming problems. SEA 2012, 11th International Symposium on Experimental Algorithms, Jun 2012, Bordeaux, France. pp 75-86, ⟨10.1007/978-3-642-30850-5_8⟩. ⟨hal-00938524⟩