رسالة جامعية
Approximations based on the method of moving asymptotes ; Approximations basées sur la méthode des asymptotes mobiles
| العنوان: | Approximations based on the method of moving asymptotes ; Approximations basées sur la méthode des asymptotes mobiles |
|---|---|
| المؤلفون: | Driouch, Abderrazak |
| المساهمون: | Laboratoire de Mathématiques et de leurs Applications Pau (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Université de Pau et des Pays de l'Adour, Université Ibn Tofail. Faculté des sciences de Kénitra, Allal Guessab |
| المصدر: | https://theses.hal.science/tel-03384750Test ; Algebraic Geometry [math.AG]. Université de Pau et des Pays de l'Adour; Université Ibn Tofail. Faculté des sciences de Kénitra, 2020. English. ⟨NNT : 2020PAUU3043⟩. |
| بيانات النشر: | HAL CCSD |
| سنة النشر: | 2020 |
| المجموعة: | HAL e2s UPPA (Université de Pau et des Pays de l'Adour) |
| مصطلحات موضوعية: | Nonlinear optimization, Non-convex optimization, Method of moving asymptotes, Large scale optimization, Topology optimization, Global convergence, Sequential convex programming, Optimisation non linéaire et non convexe, Méthode des asymptotes mobiles, Optimisation à grande échelle et topologique, Convergence globale, Programmation séquentiel convexe, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] |
| الوصف: | The method of moving asymptotes (MMA) is widely used for minimizing a continuous function of several variables. At each iterate of this method, the objective function and the constraints of the optimization problem are approximated by a rational convex function. To ensure the convergence of the MMA method, the sub problem of each iteration needs to be solved to its unique global optimal. This method formulates separable and strictly convex nonlinear sub problems iteratively. Lower and upper asymptotes are introduced to truncate the feasible region. Due to the special structure, the resulting sub problems can be solved by numerous efficient nonlinear optimization methods, for example, interior-point methods (IPM) and sequential convex programming (SCP). The original version of the Method of Moving Asymptotes (MMA) is not guaranteed to be in the corresponding feasible region described by the constraints. As a consequence, it is not able to solve the optimization problems where the feasible region defined by the constraints of feasibility. We propose in this thesis a new approximations and algorithms for unconstrained optimization, easy to implement based on the method of moving asymptotes, have the same advantages of the original version of the MMA and the SCP, and more advantages of global convergence, and we do not need to solve the sub problems generated by other classical methods thanks to their explicit solutions. We compare the resulting algorithms with known methods like Newton’s method and the Gradient projection method (GP). An extension of the MMA using the spectral parameters instead of the second-order information is presented; these parameters keep the generated sequence conveniently conservative with respect to the original functions and give information about the curvature, preserving the global convergence property. As far as the objective function, conservative approximations ensure monotonically decreasing values. Strict convexity and separability of the model functions are kept so that the sub ... |
| نوع الوثيقة: | doctoral or postdoctoral thesis |
| اللغة: | English |
| العلاقة: | NNT: 2020PAUU3043; tel-03384750; https://theses.hal.science/tel-03384750Test; https://theses.hal.science/tel-03384750/documentTest; https://theses.hal.science/tel-03384750/file/thesisdriouch.pdfTest |
| الإتاحة: | https://theses.hal.science/tel-03384750Test https://theses.hal.science/tel-03384750/documentTest https://theses.hal.science/tel-03384750/file/thesisdriouch.pdfTest |
| حقوق: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.DC95884F |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |