  In this paper, we consider lasso problems with zero-sum constraint, commonly
required for the analysis of compositional data in high-dimensional spaces. A
novel algorithm is proposed to solve these problems, combining a tailored
active-set technique, to identify the zero variables in the optimal solution,
with a 2-coordinate descent scheme. At every iteration, the algorithm chooses
between two different strategies: the first one requires to compute the whole
gradient of the smooth term of the objective function and is more accurate in
the active-set estimate, while the second one only uses partial derivatives and
is computationally more efficient. Global convergence to optimal solutions is
proved and numerical results are provided on synthetic and real datasets,
showing the effectiveness of the proposed method. The software is publicly
available.
