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Fan, J.Y. and Yuan, Y.X. (2005) On the Quadratic Convergence of the Levenberg-Marquardt Method without Nonsingularity Assumption. Computing, 74, 23-39.
http://dx.doi.org/10.1007/s00607-004-0083-1

has been cited by the following article:

• TITLE: A Regularized Newton Method with Correction for Unconstrained Convex Optimization

  AUTHORS: Liming Li, Mei Qin, Heng Wang

  KEYWORDS: Regularied Newton Method, Correction Technique, Trust Region Technique, Unconstrained Convex Optimization

  JOURNAL NAME: Open Journal of Optimization, Vol.5 No.1, March 15, 2016

  ABSTRACT: In this paper, we present a regularized Newton method (M-RNM) with correction for minimizing a convex function whose Hessian matrices may be singular. At every iteration, not only a RNM step is computed but also two correction steps are computed. We show that if the objective function is LC2, then the method posses globally convergent. Numerical results show that the new algorithm performs very well.