Author(s)

Liming Li, Mei Qin^*, Heng Wang

College of Science, University of Shanghai for Science and Technology, Shanghai, China.

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.

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

Li, L. , Qin, M. and Wang, H. (2016) A Regularized Newton Method with Correction for Unconstrained Convex Optimization. Open Journal of Optimization, 5, 44-52. doi: 10.4236/ojop.2016.51006.