Cubic Regularization Method

Subsampled cubic regularization method with distinct sample sizes for function, gradient, and Hessian

  • Max L. N. Gonçalves
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    We develop and study a subsampled cubic regularization method for finite-sum composite optimization problems, in which the function, gradient, and Hessian are estimated using possibly different sample sizes. By allowing each quantity to have its own sampling strategy, the proposed method offers greater flexibility to control the accuracy of the model components and to better … Read more

    Subsampled cubic regularization method for finite-sum minimization

  • Max L. N. Gonçalves
    • Categories Global Optimization, Nonlinear Optimization Tags , ,

    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. … Read more