Optimisation globale de polynômes en variables mixte-entières

Arnaud Lazare 1, 2
1 CEDRIC - OC - CEDRIC. Optimisation Combinatoire
CEDRIC - Centre d'études et de recherche en informatique et communications
Abstract : In this thesis, we are interested in the study of polynomial programs. These problems have many practical applications and are currently actively studied, but they remain very difficult and only small instances are addressed. In most of this manuscript, we study optimization problems with binary variables. We propose several convex reformulations for these problems. We first focus on linearizations by introducing the concept of q−linearization. Then, we apply convex reformulation to the polynomial problem. We then extend quadratic convex reformulation to the polynomial case. We propose several new reformulations that we compare to existing methods on instances of the literature. In particular we present method PQCR for unconstrained binary polynomial problems, which is able to solve several unsolved instances. We also propose a theoretical study to compare the different quadratic reformulations of the literature and then apply a convex reformulation to them. Finally, we consider more general problems and we propose a method to compute convex relaxations for problems with continuous variables.
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Arnaud Lazare. Optimisation globale de polynômes en variables mixte-entières. Recherche opérationnelle [cs.RO]. École doctorale de mathématiques Hadamard (EDMH, ED 574), 2019. Français. ⟨tel-02462537⟩

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