Department of Applied Mathematics & Physics, Kyoto University

### Technical Report 2009-020 (December 14, 2009) On a Global Complexity Bound of the Levenberg-Marquardt Method by Kenji Ueda and Nobuo Yamashita

In this paper, we investigate a global complexity bound of the Levenberg-Marquardt method (LMM) for the nonlinear least squares problem. The global complexity bound for an iterative method solving unconstrained minimization of $\phi$ is an upper bound on the number of iterations required to get an approximate solution such that $\|\nabla \phi (x)\| \le \epsilon$. We show that the global complexity bound of the LMM is $O(\epsilon^{-2})$.