The Gauß-Newton Method and its Implementation in the Optimization Library Oppy

Abstract

This thesis provides a detailed description of the Gauß-Newton method, which is a common and effective technique for solving least-squares problems. A proof of its linear and locally quadratic convergence is presented. Additionally, the Levenberg-Marquardt method is discussed as a variant of the Gauß-Newton approach. Furthermore, a new implementation of the mentioned optimization techniques and its embedding into the Python library oppy is introduced. Two distinct application cases are performed and evaluated, which adopt the formerly presented theoretical considerations and demonstrate the effectiveness of the applied methods.