A Sub-Additive DC Approach to the Complementarity Problem

Tangi Migot (1, 2) , Lina Abdallah (3) , Mounir Haddou (1, 2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 INSA Rennes - Institut National des Sciences Appliquées - Rennes
3 LU / ULB - الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth]

In this article, we propose a new merit function based on sub-additive functions for solving a general complementarity problem. This leads to consider an optimization problem that is equivalent to the NCP. In the case of a concave NCP this optimization problem is a Difference of Convex (DC) program and we can therefore use DC Algorithm to locally solve it. We prove that in the case of a monotone NCP, it is sufficient to compute a stationary point of the optimization problem to get a solution of the complementarity problems. In the case of a general NCP, assuming that a DC decomposition of the complementarity problem is known, we propose a penalization technique to reformulate the optimization problem as a DC program. Numerical results on linear complementarity problems and absolute value equations show that our method is promising.

Mots clés: dc algorithm; merit function; complementarity problem; difference of convex

Domaines: Optimisation et contrôle [math.OC]

Tangi Migot, Lina Abdallah, Mounir Haddou. A Sub-Additive DC Approach to the Complementarity Problem. Computational Optimization and Applications, 2019, 73 (2), pp.509-534. ⟨10.1007/s10589-019-00078-w⟩. ⟨hal-01609835v2⟩