Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/32178
Title: Regularized Newton methods for convex minimization problems with singular solutions
Authors: Li, DH
Fukushima, M
Qi, L 
Yamashita, N
Keywords: Global convergence
Minimization problem
Quadratic convergence
Regularized newton methods
Unit step
Issue Date: 2004
Publisher: Springer
Source: Computational optimization and applications, 2004, v. 28, no. 2, p. 131-147 How to cite?
Journal: Computational optimization and applications 
Abstract: This paper studies convergence properties of regularized Newton methods for minimizing a convex function whose Hessian matrix may be singular everywhere. We show that if the objective function is LC2, then the methods possess local quadratic convergence under a local error bound condition without the requirement of isolated nonsingular solutions. By using a backtracking line search, we globalize an inexact regularized Newton melhod. We show that the unit stepsize is accepted eventually. Limited numerical experiments are presented, which show the practical advantage of the method.
URI: http://hdl.handle.net/10397/32178
ISSN: 0926-6003
EISSN: 1573-2894
DOI: 10.1023/B:COAP.0000026881.96694.32
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