Subsampled cubic regularization method for finite-sum minimization

This paper proposes and analyzes  a  subsampled Cubic Regularization Method  (CRM) for solving  finite-sum optimization problems.  The new method uses  random subsampling techniques  to approximate  the  functions, gradients and Hessians in order to reduce the overall computational cost of the CRM. Under suitable hypotheses,  first- and second-order  iteration-complexity bounds and global convergence analyses  are presented. We also discuss the local convergence properties of the method.    Numerical experiments are presented to illustrate the performance of the proposed scheme.

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