“…When p = 1 or p = ∞, this problem can be solved using linear programming. More generally, when p / ∈ {1, ∞}, the problem is nonlinear, and multiple approaches have been developed for solving it, including, e.g., a homotopy-based solver [Bubeck et al, 2018], solvers based on iterative refinement [Adil et al, 2019a, Adil andSachdeva, 2020], and solvers based on the classical method of iteratively reweighted least squares [Ene andVladu, 2019, Adil et al, 2019b]. Such solvers typically rely on fast linear system solves and attain logarithmic dependence on the inverse accuracy 1/ǫ, at the cost of iteration count scaling polynomially with one of the dimensions of A (typically the lower dimension, which is equal to the number of rows m), each iteration requiring a constant number of linear system solves.…”