Levenberg-Marquardt Algorithms for Nonlinear Equations, Multi-objective Optimization, and Complementarity Problems

The Levenberg-Marquardt algorithm is a classical method for solving nonlinear systems of equations that can come from various applications in engineering and economics. Recently, Levenberg-Marquardt methods turned out to be a valuable principle for obtaining fast convergence to a solution of the nonlinear system if the classical nonsingularity assumption is replaced by a weaker error bound condition. In this way also problems with nonisolated solutions can be treated successfully. Such problems increasingly arise in engineering applications and in mathematical programming. In this thesis we use Levenberg-Marquardt algorithms to deal with nonlinear equations, multi-objective optimization and complementarity problems. We develop new algorithrris for solving these problems and investigate their convergence properties.