On the Rate of Convergence of the Levenberg-Marquardt Method

By Nobuo Yamashita, Masao Fukushima. 2001

453 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b85c82404fe43760a6d1d117f84effdd34b6d44d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Newton Sketch: A Near Linear-Time Optimization Algorithm with Linear-Quadratic Convergence (2015, methodology): “Even for functions that are weakly convex—that is, convex but not strongly convex—modifications of Newton’s method have superlinear convergence (for instance, see the paper [39] for an analysis of the Levenberg–Marquardtmethod).”
Levenberg–Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints (2004, background): “These lemmas can be derived by suitable modi5cations of the corresponding unconstrained results in [24].”
Deriving Merchantable Volume in Poplar through a Localized Tapering Function from Non-Destructive Terrestrial Laser Scanning (2016, methodology): “ISBN1-56827-390-8), using the Levenberg-Marquardt (L-M) least squares fitting technique, an algorithm for solving generic curve-fitting problems [28,29].”
Superlinear Convergence of a Newton-Type Algorithm for Monotone Equations (2005, background): “Proof. By ( 4 ) and Lemma 3.3, for all k sufficiently large,”
A Nonsmooth L-M Method for Solving the Generalized Nonlinear Complementarity Problem over a Polyhedral Cone (2005, methodology): “To guarantee the superlinear (quadratic) convergence of the L-M method for solving a system of equations H(x) = 0, Yamashita and Fukushima provided a weaker condition than nonsingularity of the Jacobian recently [24], which requires that the local error bound of H(x) holds near a solution point x∗, ”
An efficient Levenberg–Marquardt method with a new LM parameter for systems of nonlinear equations (2018, methodology): “In [11], Fan and Yuan extended the results in [10] by proposing λk = ‖F(xk)‖, and proved that a similar convergence property is satisfied.”
On the inexactness level of robust Levenberg–Marquardt methods (2010, methodology): “Levenberg–Marquardt (LM) methods for solving Equation (1) are known ([11]) to possess superlinear convergence properties, if the starting point is sufficiently close to some z*2Z*, and if a certain local error bound condition holds.”