Truncated regularized Newton method for convex minimizations

Authors:
Ying-Jie Li;Dong-Hui Li
Affiliations:
College of Mathematics and Econometrics, Hunan University, Changsha, China 410082;College of Mathematics and Econometrics, Hunan University, Changsha, China 410082
Venue:
Computational Optimization and Applications
Year:
2009

Citing 6
Cited 1

A survey of truncated-Newton methods

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Regularized Newton Methods for Convex Minimization Problems with Singular Solutions

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On the convergence of a modified regularized Newton method for convex optimization with singular solutions

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Abstract

Recently, Li et al. (Comput. Optim. Appl. 26:131---147, 2004) proposed a regularized Newton method for convex minimization problems. The method retains local quadratic convergence property without requirement of the singularity of the Hessian. In this paper, we develop a truncated regularized Newton method and show its global convergence. We also establish a local quadratic convergence theorem for the truncated method under the same conditions as those in Li et al. (Comput. Optim. Appl. 26:131---147, 2004). At last, we test the proposed method through numerical experiments and compare its performance with the regularized Newton method. The results show that the truncated method outperforms the regularized Newton method.