A decomposition method for lasso problems with zero-sum constraint

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, identify zero variables optimal solution, 2-coordinate descent scheme. At every iteration, chooses between two different strategies: first one requires compute whole gradient smooth term objective function and more accurate estimate, while second only uses partial derivatives computationally efficient. Global convergence solutions proved numerical results are provided on synthetic real datasets, showing effectiveness method. The software publicly available.