The dual IRLS scheme for (hyper-)graph $p$-Laplacians and ${\mathrm{\ell }}^p$ regression with large exponents

We introduce an iterative scheme for discrete convex minimization problems of $p$-Laplace type such as variational graph $p$-Laplace problems and ${\mathrm{\ell }}^p$ regression. In each iteration, the scheme solves only a weighted least-squares problem. We verify linear convergence for suitably regularized problems and derive convergence to any prescribed tolerance.