This dissertation considers the composite saddle-point (CSP) problem which is motivated by real-world applications in the areas of machine learning and image processing. Two new accelerated algorithms for solving composite saddle-point problems are introduced. Due to the two-block structure of the CSP problem, it can be solved by any algorithm belonging to the block-decomposition hybrid proximal extragradient (BD-HPE) framework. The framework consists of a family of inexact proximal point methods for solving a general two-block structured monotone inclusion problem which, at every iteration, solves two prox sub-inclusions according to a certain relative error criterion. By exploiting the fact that the two prox sub-inclusions in the context of the CSP problem are equivalent to two composite convex programs, the first part of this dissertation proposes a new instance of the BD-HPE framework that approximately solves them using an accelerated gradient method. It is shown that this new instance has better iteration-complexity than the previous ones. The second part of this dissertation introduces a new algorithm for solving a special class of CSP problems. The new algorithm is a special instance of the hybrid proximal extragradient (HPE) framework in which a Nesterov's accelerated variant is used to approximately solve the prox subproblems. One of the advantages of the this method is that it works for any constant choice of proximal stepsize. Moreover, a suitable choice of the latter stepsize yields a method with the best known (accelerated inner) iteration complexity for the aforementioned class of saddle-point problems. Experiment results on both synthetic CSP problems and real-world problems show that the two method significantly outperform several state-of-the-art algorithms.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24264号 / 情博第808号 / 新制||情||136(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 山下 信雄, 准教授 福田 秀美, 教授 太田 快人 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Cette thèse aborde la problématique de la conception optimale de structures composites stratifiées d’épaisseur variable. Les variables d’empilement définissent un problème d’optimisation combinatoire et des espaces de décisions de grande taille et potentiellement multimodaux. Les algorithmes d’optimisation stochastiques permettent de traiter ce type de problème et de tirer profit des performances et de l’anisotropie des plis composites pour l’allègement des structures composites stratifiées. Le but de cette étude est double : (i) développer un algorithme d’optimisation dédié aux composites stratifiés d’épaisseur variable et (ii) estimer le potentiel des composites stratifiés pour la maîtrise des performances aérodynamiques d’une pale de CROR composite.Dans la première partie de cette thèse, un algorithme évolutionnaire est spécialisé pour l’optimisation de tables de drapage et la gestion d’un ensemble de règles de conception représentatif des pratiques de l’industrie. Pour se faire, un encodage spécifique des solutions est proposé et des opérateurs de variations spécialisés sont développés.Dans la deuxième partie, l’algorithme est enrichi d’une technique de guidage basée sur l’exploitation d’un espace auxiliaire afin d'accroître son efficacité et d’intégrer davantage de connaissances des composites dans la résolution du problème.Finalement, la méthode est appliquée pour la conception d’une pale de CROR composite à l’échelle de la maquette de soufflerie. Au préalable, des processus itératifs de mise à froid et mise à chaud de la pale sont mis en place afin d’estimer la forme de la pale au repos et l’état de contraintes dans la pale en fonctionnement. / This thesis deals with the optimal design of variable-thickness laminated composite structures. The stacking variables define a combinatorial optimization problem and large decision spaces which are potentially multimodal. Stochastic optimization algorithms allow solving this type of problem and allow taking advantage from the performance and the anisotropic nature of unidirectional composite plies to lighten laminated composite structures.The purpose of this study is twofold: (i) developing an optimization algorithm dedicated to variable-thickness laminated composites and (ii) assessing the potential of laminated composites in influencing the aerodynamic performances of a composite CROR blade.Firstly, an evolutionary algorithm is specialized in order to optimize layup tables and handle a set of design guidelines which is representative of industrial practices. In this purpose, a specific encoding of the solutions is suggested and specialized variation operators are developed.Secondly, the algorithm is enriched with a guiding technique based on the exploitation of an auxiliary space in order to improve its efficiency and to include further composites-related knowledge for the resolution of the problem.Finally, the method is applied for the design of a reduced-scale composite CROR blade intended for wind-tunnel testing. Beforehand, iterative processes are implemented to estimate the shape of the non-operating blade and the stress state within the operating blade.

Indiana University-Purdue University Indianapolis (IUPUI) / In a multifidelity structural design process, depending on the required analysis, different levels of structural models are needed. Within the aerospace design, analysis and optimization community, there is an increasing demand for automatic generation of parametric feature tree (build recipe) attributed multidisciplinary models. Currently, this is mainly done by creating separate models for different disciplines such as mid-surface model for aeroelasticity, outer-mold line for aerodynamics and CFD, and built-up element model for structural analysis. Since all of these models are built independently, any changes in design parameters require updates on all the models which is inefficient, time-consuming and prone to deficiencies. In this research, Engineering Sketch Pad (ESP) is used to create attribution and maintain consistency between structural models with different fidelity levels. It provides the user with the ability to interact with a configuration by building and/or modifying the design parameters and feature tree that define the configuration. ESP is based an open-source constructive solid modeler, named OpenCSM, which is built upon the OpenCASCADE geometry kernel and the EGADS geometry generation system. The use of OpenCSM as part of the AFRL’s CAPS project on Computational Aircraft Prototype Syntheses for automatic commercial and fighter jet models is demonstrated. The rapid generation of parametric aircraft structural models proposed and developed in this work will benefit the aerospace industry with coming up with efficient, fast and robust multidisciplinary design standardization of aircraft structures. Metallic aircraft wings are usually not optimized to their fullest potential due to shortage of development time. With roughly \$1000 worth of potential fuel savings per pound of weight reduction over the operational life of an aircraft, airlines are trying to minimize the weight of aircraft structures. A stiffness based strategy is used to map the nodal data of the lower-order fidelity structural models onto the higher-order ones. A simple multi-fidelity analysis process for a parametric wing is used to demonstrate the advantage of the approach. The loads on the wing are applied from a stick model as is done in the industry. C program is created to connect the parametric design software ESP, analysis software Nastran, load file and design configuration file in CSV format. This problem gets compounded when it comes to optimization of composite wings. In this study, a multi-level optimization strategy to optimize the weight of a composite transport aircraft wing is proposed. The part is assumed to initially have some arbitrary number of composite super plies. Super plies are a concept consisting of a set of plies all arranged in the same direction. The thickness and orientation angles of the super plies are optimized. Then, each ply undergoes topometry optimization to obtain the areas of each super ply taking the least load so that it could be cut and removed. Each of the super plies are then optimized for the thickness and orientation angles of the sub plies. The work presented on this paper is part of a project done for Air Force Research Laboratory (AFRL) connecting the parametric geometry modeler (ESP) with the finite element solver (Nastran).