  Convex and nonconvex finite-sum minimization arises in many scientific
computing and machine learning applications. Recently, first-order and
second-order methods where objective functions, gradients and Hessians are
approximated by randomly sampling components of the sum have received great
attention. We propose a new trust-region method which employs suitable
approximations of the objective function, gradient and Hessian built via random
subsampling techniques. The choice of the sample size is deterministic and
ruled by the inexact restoration approach. We discuss local and global
properties for finding approximate first- and second-order optimal points and
function evaluation complexity results. Numerical experience shows that the new
procedure is more efficient, in terms of overall computational cost, than the
standard trust-region scheme with subsampled Hessians.
