A Modified Regularized Newton Method for Unconstrained Convex Optimization.

In this paper, we present a modified regularized Newton method (M-RNM) 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 local quadratic convergence under a local error bound condition. A globally convergent M-RNM algorithm is also given by using trust region technique. [ABSTRACT FROM AUTHOR]