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Contributions aux méthodes numériques pour les problèmes de complémentarité et problèmes d'optimisation sous contraintes de complémentarité

Abstract : In this thesis, we studied the regularization methods for the numerical resolution of problems with equilibria. In the first part, we focused on the complementarity problems through two applications that are the absolute value equation and the sparse optimization problem. In the second part, we concentrated on optimization problems with complementarity constraints. After studying the optimality conditions of this problem, we proposed a new regularization method, so-called butterfly relaxation. Then, based on an analysis of the regularized sub-problems we defined an algorithm with strong convergence property. Throughout the manuscript, we concentrated on the theoretical properties of the algorithms as well as their numerical applications. In the last part of this document, we presented numerical results using the regularization methods for the mathematical programs with complementarity constraints.
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Tangi Migot. Contributions aux méthodes numériques pour les problèmes de complémentarité et problèmes d'optimisation sous contraintes de complémentarité. Analyse numérique [math.NA]. INSA de Rennes, 2017. Français. ⟨NNT : 2017ISAR0026⟩. ⟨tel-01791526⟩

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