Modified Levenberg Marquardt algorithm for inverse problems

Abstract

The Levenberg Marquardt (LM) algorithm is a popular non-linear least squares optimization technique for solving data matching problems. In this method, the damping parameter plays a vital role in determining the convergence of the system. This damping parameter is calculated arbitrarily in the classical LM, causing it to converge prematurely when used for solving real world engineering problems. This paper focuses on changes made to the classical LM algorithm to enhance its performance. This is achieved by adaptive damping, wherein the damping parameter is varied depending on the convergence of the objective function. To eliminate the need for a good initial guess, the idea of using an evolutionary algorithm in conjunction with the LM algorithm is also explored. © 2010 Springer-Verlag.