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

Abstract: We introduce an iterative scheme for discrete convex minimization problems of $p$-Laplace type such as variational graph $p$-Laplace problems and $\ell^p$ 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.