A Subsampled cubic regularization trust regionmethod

Abstract

This paper studies the solution of unconstrained optimization problems based on trust region methods with simple subproblem, in which approximations to the gradient and Hessian are calculated through subsampling. In this framework, We propose a new adaptive rule for updating the radius. Also, in order to improve the efficiency of the algorithm, we try to use more available information of function values and gradient, as soon as possible. In this regard, we introduced a scalar approximation of the Hessian at the current point using a modified quasi-Newton equation. Specifically, we focus our attention on a variant of trust region methods known as cubic regularization. By employing a suitable sampling scheme, we establish the local and global convergence properties.