  We adapt the gradient sampling algorithm to the local scoring algorithm to
solve complex estimation problems based on an optimization of an objective
function. This overcomes non-differentiability and non-smoothness of the
objective function. The new algorithm estimates the Clarke generalized
subgradient used in the local scoring, thus reducing numerical instabilities.
The method is applied to quantile regression and to the peaks-over-threshold
method, as two examples. Real applications are provided for a retail store and
temperature data analysis.
