  We propose a trust-region method for finite-sum minimization with an adaptive
sample size adjustment technique, which is practical in the sense that it leads
to a globally convergent method that shows strong performance empirically
without the need for experimentation by the user. During the optimization
process, the size of the samples is adaptively increased (or decreased)
depending on the progress made on the objective function. We prove that after a
finite number iterations the sample includes all points from the data set and
the method becomes a full-batch trust-region method. Numerical experiments on
convex and nonconvex problems support our claim that our algorithm has
significant advantages compared to current state-of-the-art methods.
