Good and Fast Row-Sparse ah-Symmetric Reflexive Generalized Inverses

We construct sparse and structured generalized inverses, with application to the efficient computation of least-squares solutions of inconsistent systems of linear equations. Leveraging formulations from Ponte, Fampa, Lee and Xu (2024) to minimize the 1- and 2,1-norms of generalized inverses that satisfy important properties of the Moore-Penrose pseudoinverse, we develop efficient and scalable ADMM algorithms to address these norms minimization, and to limit the number of non-zero rows in the solution. We prove 2,1-norm approximation results for a local-search procedure of Xu, Fampa, Lee and Ponte (2021) and compare the ADMM algorithms with the local-search procedure and optimization solvers.