Modélisation et optimisation non convexe basées sur la programmation DC et DCA pour la résolution de certaines classes des problèmes en fouille de données et cryptologie

Abstract : This thesis is dedicated to non-convex modeling and the optimization based on the DC programming and DCA for certain classes of problems of two important domains : the Data Mining and the Cryptology. They are non-convex optimization problems of very large dimensions for which the research of good solution methods is always of actuality. Our work is based mainly on the DC programming and DCA that have been successfully applied in various fields of applied sciences, including machine learning. It is motivated and justified by the robustness and the good performance of DC programming and DCA in comparison with the existing methods. This thesis is devised in three parties. The first part, entitling Methodology, serves as a reference for other chapters. The first chapter concerns the programming of DC and DCA while the second chapter describes the genetic algorithms. In the second part, we develop the DC and DCA programming to solve two classes of problems in Data Mining. In the chapter four, we take consideration into the model of classification FCM and develop the programming DC and DCA for their resolution. Many formulations DC in correspondence to different decompositions DC are proposed. Our work in hierarchic classification (chapter 5) is motivated by one of its interesting and very important applications, known as muliticast communication. It's a non-convex, non differentiable, non-convex problem in a very big dimension with which we have reformulated in the forms of 3 different DC programs and developed the DCA relative. The 3rd part focuses on the Cryptology. The 1st chapter is the construction of stable boonlean functions with high degree of non-linearity - one of the crucial problems of Cryptography. Many versions of combination of 2 approaches, DCA and Genetic Algorithms (GA) are studied in the purpose of exploiting simultaneously the efficacy of each approach. The secondrd work is about the techinics of cryptanalyse of a identification scheme based on two problems Perceptron (PP) and Perceptron Permuted. We propose a method of resolving two problems PP and PPA by DCA and a cutting plan method in the last chapter
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Hoai Minh Le. Modélisation et optimisation non convexe basées sur la programmation DC et DCA pour la résolution de certaines classes des problèmes en fouille de données et cryptologie. Ordinateur et société [cs.CY]. Université Paul Verlaine - Metz, 2007. Français. 〈NNT : 2007METZ054S〉. 〈tel-01749011〉

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