Department of Applied Mathematics & Physics, Kyoto University
Technical Report 2001-001 (January 16, 2001)
Convergence Properties of the Inexact Levenberg-Marquardt Method under Local Error Bound Conditions
by Hiroshige Dan, Nobuo Yamashita and Masao Fukushima
In this paper, we consider convergence properties of
the Levenberg-Marquardt method for solving nonlinear equations.
It is well-known that the nonsingularity of Jacobian at a solution
guarantees that the Levenberg-Marquardt method
has a quadratic rate of convergence.
Recently, Yamashita and Fukushima showed that
the Levenberg-Marquardt method has a quadratic rate
of convergence under the assumption of local error bound,
which is milder than the nonsingularity of Jacobian.
In this paper, we show that the inexact Levenberg-Marquardt method (ILMM),
which does not require computing exact search directions,
has a superlinear rate of convergence under the same assumption
of local error bound.
Moreover, we propose the ILMM with Armijo's stepsize rule
that has global convergence under mild conditions.