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Contribution to numerical optimization with applications to engineering problems

Diouane, Youssef Contribution to numerical optimization with applications to engineering problems. (2021) [HDR]

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Abstract

The rapid development of artificial intelligence and computational sciences has attracted much more attention from researchers and practitioners to numerical optimization. In this manuscript our goal is to propose competitive numerical optimization methods with demonstrable performances on a variety of application problems from data assimilation, aircraft design or data science. More specifically, our contribution to the field of numerical optimization addresses the following three challenges. The first challenge is related to optimization problems where the derivative information is not available or hard to obtain in practice. We will show how ideas from deterministic derivative free optimization can improve the efficiency and the rigorousness of a class of evolution strategies. Our proposed framework achieves rigorously global convergence under reasonable assumptions. The obtained method is also extended to handle general constrained optimization problems. The second challenge is related to the Levenberg-Marquardt algorithm (LM) which is one of the most popular algorithms for the solution of nonlinear least squares problems. Motivated by exploiting the problem structure in data assimilation, we consider solving general nonlinear least-squares problems where one may have a solution with a non zero residual. We will present and analyze the convergence properties of a novel LM method that carefully balances the opposing objectives of ensuring global convergence and stabilizing a fast local convergence regime. An extension of the proposed framework to solve large-scale constrained inverse problems is also proposed. The third challenge is related to optimization problems arising in machine learning or in parameter identification, where it can be computationally challenging or even infeasible to evaluate the exact objective function or its derivatives. The presence of noise is particularly challenging for most of the classical optimization methods. In this context, we will discuss novel methods with both favorable convergence properties and satisfactory practical performance. Finally, we will present algorithmic and computational aspects to solve engineering optimization problems related to structural and aircraft design efficiently.

Item Type:HDR
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Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
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Deposited On:18 May 2022 07:45

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