A Regularized Newton Method with Correction for Unconstrained Nonconvex Optimization

  •  Heng Wang    
  •  Mei Qin    


In this paper, we present a modified regularized Newton method for minimizing a nonconvex function whose Hessian matrix may be singular. We show that if the gradient and Hessian of the objective function are Lipschitz continuous, then the method has a global convergence property. Under the local error bound condition which is weaker than nonsingularity, the method has cubic convergence.

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