Neste trabalho o autor programa e avalia algoritmos para análise e otimização de pressão sonora desenvolvidos para sistemas acoplados vibroacústicos, verificando o desempenho da análise da resposta e comparando a adequação dos algoritmos de Programação Quadrática Sequencial (SQP - Sequencial Quadratic Programming) e Genético na otimização da resposta. A otimização da resposta é implementada no programa acadêmico de elementos finitos Meflab, e utiliza para otimização a função fmincon disponível no programa comercial Matlab®. Igualmente a otimização da resposta é implementada através de um código desenvolvido de algoritmos genéticos. Para os casos acoplados estudados o algoritmo SQP mostra uma redução da pressão sonora inicial inferior ao algoritmo Genético, para casos desacoplados o método SQP consegue reduções maiores. Os resultados foram validados através de formulações analíticas disponíveis e comparados em alguns casos com soluções de programas comerciais. / In this work the author implements in a software and evaluates algorithms for analysis and optimization of the sound pressure developed for coupled vibroacoustic systems, checking the performance and response analysis comparing the suitability of the Sequencial Quadratic Programming (SQP) and Genetic algorithms in optimizing response. The optimization of the response is implemented in the academic program Meflab finite element, and uses optimization function fmincon available in the commercial program Matlab ®. Also the optimization of the response is implemented through a code developed genetic algorithms. For the coupled cases studied the SQP algorithm recduce less the inicial sunde pressure tha Genetic algorithm, for uncoupled cases SQP method has a bigger reduccion. The results were validated by analytical formulations available in some cases and compared with commercial software solutions.

A new optimization algorithm, which can efficiently solve large-scale constrained non-linear optimization problems and leverage parallel computing, is designed and studied. The new algorithm, referred to herein as LASO or LArge Scale Optimizer, combines the best features of various algorithms to create a computationally efficient algorithm with strong convergence properties. Numerous algorithms were implemented and tested in its creation. Bound-constrained, step-size, and constrained algorithms have been designed that push the state-of-the-art. Along the way, five novel discoveries have been made: (1) a more efficient and robust method for obtaining second order Lagrange multiplier updates in Augmented Lagrangian algorithms, (2) a method for directly identifying the active constraint set at each iteration, (3) a simplified formulation of the penalty parameter sub-problem, (4) an efficient backtracking line-search procedure, (5) a novel hybrid line-search trust-region step-size calculation method. The broader impact of these contributions is that, for the first time, an Augmented Lagrangian algorithm is made to be competitive with state-of-the-art Sequential Quadratic Programming and Interior Point algorithms. The present work concludes by showing the applicability of the LASO algorithm to simulate one step of digital human walking and to accelerate the optimization process using parallel computing.

An optimal control problem governed by the heat equation with nonlinear boundary conditions is considered. The objective functional consists of a quadratic terminal part and a quadratic regularization term. It is known, that an SQP method converges quadratically to the optimal solution of the problem. To handle the quadratic optimal control subproblems with high precision, very large scale mathematical programming problems have to be treated. The constrained problem is reduced to an unconstrained one by a method due to Bertsekas. A multigrid approach developed by Hackbusch is applied to solve the unconstrained problems. Some numerical examples illustrate the behaviour of the method.

In this paper two basic SQP-approaches for solving implicitly defined inverse problems are presented. Such problems often arises in parameter identification for differential equations. We also include regularization strategies which differ from similar problems in Optimal control. The main focus is on formulating saddle point problems for calculating the next iterate. Conditions for the unique and stable solvability of these problems are presented. The analytical considerations are illustrated by two examples including their discretizations and a numerical case study.

Cette thèse traite le développement d'un modèle mathématique d'optimisation acoustique des trajectoires de vol de deux avions commerciaux en approche sous contrainte énergétique, aérodynamique et opérationnelle. C'est un modèle analytique de contrôle optimal non-linéaire et non-convexe régi par un système d'équations différentielles ordinaires issues de la dynamique de vol et des contraintes associées. Notre contribution porte sur la modélisation mathématique des équations, l'optimisation et la programmation algorithmique d'un modèle d'optimisation non-linéaire du bruit de deux avions en approche simultanée. Les points abordés sont le développement mathématique du modèle 3D "exact" de leur dynamique de vol, la modélisation mathématique de la commande optimale de ce système dynamique, l'introduction de la consommation du carburant par les avions comme une équation différentielle avec une fonction consommation spécifique variable en fonction de l'évolution de leur dynamique, la modélisation mathématique instantanée de la fonction objectif représentant le bruit global des deux avions en approche. Sa résolution porte sur la méthode directe de programmation séquentielle quadratique avec régions de confiance sous AMPL et KNITRO. Une méthode indirecte a été appliquée sous le principe de maximum de Pontryagin suivie d'une discrétisation de type Runge-Kutta partition-née symplectique d'ordre 4 afin de démontrer la commutation entre l'approche directe et l'approche indirecte. Les résultats obtenus confirment des trajectoires optimales en descente continue, réduisant le bruit au sol ainsi que la consommation de kérosène de deux avions