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

TL;DR

The paper presents a new iterative scheme for solving convex minimization problems related to graph $p$-Laplacians and $ ext{l}^p$ regression, demonstrating linear convergence and adjustable accuracy.

Contribution

It introduces an efficient iterative method that simplifies complex $p$-Laplace problems into weighted least-squares, with proven convergence properties.

Findings

Linear convergence for regularized problems

Convergence to any prescribed tolerance

Applicable to variational graph $p$-Laplace and $ ext{l}^p$ regression

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.