Nunes Grapiglia, GeovaniTaminiau, TimothéTimothéTaminiau2025-05-142025-05-142025-05-142023https://hdl.handle.net/2078.2/32407In this thesis, we study derivative-free methods able to solve systems of nonlinear equations with a particular emphasis on the underdetermined case. We present a new class of methods which generalizes the works from Grapiglia and Chorobura [11] and Echebest, Schuverdt, and Vignau [9]. If the Jacobian corresponding to the system of nonlinear equations is Lipschitz continuous then we prove, for two particular methods belonging to this class, worst-case complexity bounds on the number of function evaluations to reach some optimality measure. Afterwards, the methods are implemented and tested numerically to observe how they behave in practice. Finally, we provide an application of these methods in the context of black-box attack against deep neural networks. In particular, we model mathematically the way to modify slightly an input such that it is misclassified with the constraint that the neural network’s structure is hidden.Underdetermined systems of nonlinear equationsDerivative-freeNonmonotone line searchBlack-box adversarial attacktext::thesis::master thesisthesis:40763