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This report comprises the first contributions from different partners on Federated Learning (FL). After a preliminary introductory section where the fundamental procedures and limitations are described, we detail the well-known mathematical foundation of Federated Learning for convex problems. In this case, we present a key algorithm, Alternating Direction Multipliers Method (ADMM), which is able to implement in a distributed way some fundamental problems such as regression (Ridge and LASSO)doi:10.5281/zenodo.5862590 fatcat:trd6rdi7pzcq7gcta62jcitwua