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Article Dans Une Revue Computational Optimization and Applications Année : 2019

A Sub-Additive DC Approach to the Complementarity Problem

Résumé

In this article, we study a merit function based on sub-additive functions for solving the non-linear complementarity problem (NCP). 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 concave monotone NCP, it is sufficient to compute a stationary point of the optimization problem to obtain a solution of the complementarity problem. 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 and prove that local minima of this penalized problem are also local minima of the merit problem. Numerical results on linear complementarity problems, absolute value equations and non-linear complementarity problems show that our method is promising.
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Dates et versions

hal-01609835 , version 1 (04-10-2017)
hal-01609835 , version 2 (02-11-2017)
hal-01609835 , version 3 (23-10-2023)

Identifiants

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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-01609835v3⟩
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