The New Butterfly Relaxation Method for Mathematical Programs with Complementarity Constraints

Jean-Pierre Dussault (1) , Mounir Haddou (2) , Tangi Migot (3)

1 UdeS - Département d'informatique [Sherbrooke]
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 IRMAR - Institut de Recherche Mathématique de Rennes

We propose a new family of relaxation schemes for mathematical program with complementarity constraints that extends the relaxations of Kadrani, Dussault, Bechakroun from 2009 and the one of Kanzow & Schwartz from 2011. We discuss the properties of the sequence of relaxed non-linear program as well as stationarity properties of limiting points. A sub-family of our relaxation schemes has the desired property of converging to an M-stationary point. We introduce a new constraint qualication to prove convergence of our method, which is the weakest known constraint qualication that ensures bounded-ness of the sequence generated by the method. A comprehensive numerical comparison between existing relaxations methods is performed on the library of test problems MacMPEC and shows promising results for our new method.

Mots clés: CRSC; constraint qualication; nonlinear programming; MPCC; relaxation methods; stationarity point; non-linear programming; MPEC; stationary point; constraint qualification

Domaines: Optimisation et contrôle [math.OC]

Jean-Pierre Dussault, Mounir Haddou, Tangi Migot. The New Butterfly Relaxation Method for Mathematical Programs with Complementarity Constraints. 2016. ⟨hal-01525399v4⟩