Truncated regularized Newton method for convex minimizations

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.