Optimization techniques for non differentiable equality and inequality systems

Abstract

This thesis presents a numerical study for solving systems of nonlinear equations and inequalities. We use global optimization methods to solve these nonlinear systems of Lipschitz and Hölder functions that cannot be handled using traditional numerical methods. We also focus on the Alienor method, which relies on reducing the dimension of the initial global optimization problem with several variables to a single-variable problem using α-dense curves. We provide some numerical applications of these methods.