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This paper deals with subsampled spectral gradient methods for minimizing finite sums. Subsample function and gradient approximations are employed in order to reduce the overall computational cost of the classical spectral gradient methods. The global convergence is enforced by a nonmonotone line search procedure. Global convergence is proved provided that functions and gradients are approximated with increasing accuracy. R-linear convergence and worst-case iteration complexity is investigated in case of strongly convex objective function. Numerical results on well known binary classification problems are given to show the effectiveness of this framework and analyze the effect of different spectral coefficient approximations arising from the variable sample nature of this procedure.

Given the severe impact of COVID-19 on several societal levels, it is of crucial importance to model the impact of restriction measures on the pandemic evolution, so that governments are able to take informed decisions. Even though there have been countless attempts to propose diverse models since the raise of the outbreak, the increase in data availability and start of vaccination campaigns calls for updated models and studies. Furthermore, most of the works are focused on a very particular place or application and we strive to attain a more general model, resorting to data from different countries. In particular, we compare Great Britain and Israel, two highly different scenarios in terms of vaccination plans and social structure. We build a network-based model, complex enough to model different scenarios of government-mandated restrictions, but generic enough to be applied to any population. To ease the computational load we propose a decomposition strategy for our model.

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