  We consider unconstrained optimization problems with nonsmooth and convex
objective function in the form of mathematical expectation. The proposed method
approximates the objective function with a sample average function by using
different sample size in each iteration. The sample size is chosen in an
adaptive manner based on the Inexact Restoration. The method uses line search
and assumes descent directions with respect to the current approximate
function. We prove the almost sure convergence under the standard assumptions.
The convergence rate is also considered and the worst-case complexity of
$\mathcal{O} (\varepsilon^{-2})$ is proved. Numerical results for two types of
problems, machine learning hinge loss and stochastic linear complementarity
problems, show the efficiency of the proposed scheme.
