A Generalized Direction in Interior Point Method for Monotone Linear Complementarity Problems

Mounir Haddou (1, 2) , Tangi Migot (1, 2) , Jérémy Omer (1, 2)

1 INSA Rennes - Institut National des Sciences Appliquées - Rennes
2 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper, we present a new interior point method with full Newton step for monotone linear complementarity problems. The specificity of our method is to compute the Newton step using a modified system similar to that introduced by Darvay in 2003. We prove that this new method possesses the best known upper bound complexity for these methods. Moreover, we extend results known in the literature since we consider a general family of smooth concave functions in the Newton system instead of the square root.

Mots clés: concave functions; complementarity; interior-point methods; linear programming; linear complementarity problems; polynomial time complexity

Domaines: Optimisation et contrôle [math.OC]

Mounir Haddou, Tangi Migot, Jérémy Omer. A Generalized Direction in Interior Point Method for Monotone Linear Complementarity Problems. Optimization Letters, 2019, 13 (1), pp.35-53. ⟨10.1007/s11590-018-1241-2⟩. ⟨hal-01355566v2⟩