Regularized Newton methods for convex minimization problems with singular solutions

Computational Optimization and Applications

Volumn 28, Issue 2, 2004, Pages 131-147

  Li, Dong Hui ^a   Fukushima, Masao ^b   Qi, Lioun ^c   Yamashita, Nobuo ^b  

^a HUNAN UNIVERSITY   (China)

^b KYOTO UNIVERSITY   (Japan)

^c HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

Author keywords

Global convergence; Minimization problem; Quadratic convergence; Regularized newton methods; Unit step

Indexed keywords

BOUNDARY CONDITIONS; FUNCTIONS; MATRIX ALGEBRA; NUMERICAL METHODS; PROBLEM SOLVING; QUADRATIC PROGRAMMING;

GLOBAL CONVERGENCE; MINIMIZATION PROBLEMS; QUADRIATIC CONVERGENCE; REGULARIZED NEWTON METHODS; UNIT STEPS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 3543109143     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:COAP.0000026881.96694.32     Document Type: Article

References (5)

1. H. Dan, N. Yamashita, and M. Fukushima, "Convergence properties of the inexact Levenberg-Marquardt method under local error bound conditions," Optimization Methods and Software, vol. 17, pp. 605-626, 2002.
2. R.S. Dembo, S.C. Eisenstat, and T. Steihaug, "Inexact Newton method," SIAM Journal on Numerical Analysis, vol. 19, pp. 400-408, 1982.
3. J.Y. Fan and Y.X. Yuan, "On the convergence of a new Levenberg-Marquardt method," Technical Report, AMSS, Chinese Academy of Sciences, 2001.
4. G.W. Stewart and J.G. Sun, Matrix Perturbation Theory, Academic Press: New York, NY, 1990.
5. N. Yamashita and M. Fukushima, "On the rate of convergence of the Levenberg-Marquardt method," Computing, vol. 15(Suppl), pp. 239-249, 2001.