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Global complexity bound of the Levenberg-Marquardt method. (English) Zbl 1406.65037

Summary: In this paper, we propose a new updating rule of the Levenberg-Marquardt (LM) parameter for the LM method for nonlinear equations. We show that the global complexity bound of the new LM algorithm is \(O(\varepsilon^{-2})\), that is, it requires at most \(O(\varepsilon^{-2})\) iterations to derive the norm of the gradient of the merit function below the desired accuracy \(\varepsilon\).

MSC:

65H10 Numerical computation of solutions to systems of equations
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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