A regularized Newton method for degenerate unconstrained optimization problems

A regularized Newton method is presented in this paper to solve unconstrained nonconvex minimization problems without the nonsingularity assumption of solutions. The modified Cholesky factorization method proposed by Cheng and Higham is employed to calculate the regularized Newton step. Under suitable conditions, the global convergence of the regularized Newton method is established, and the fast local convergence result is achieved under the local error bound conditions. Some preliminary numerical results are also reported.