A Regularized Newton Method with Correction for Unconstrained Convex Optimization

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 LC 2 , then the method posses globally convergent. Numerical results show that the new algorithm performs very well.