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Felipe Guerra

Publications and source records attributed to Felipe Guerra.

2 recordsLinked to original sources
arXiv2026

Primal-dual multigrid methods for nonsmooth optimization

In optimization, one often encounters problems of the form $\min_x F(x)+E(x)+G(Kx)$. In this work, we combine primal-dual algorithms with multigrid techniques for their solution. To link the the fine-grid and coarse-grid problems problems, we introduce a nonsmooth primal-dual coherence condition, and an efficient partially linearized line search procedure. Our work is motivated by total variation regularized inverse imaging problems, on which we demonstrate the efficacy of the method, being able to solve problems not previously possible with forward-backward multigrid methods.

math.OC↗
arXiv2025

Multigrid methods for total variation

Based on a nonsmooth coherence condition, we construct and prove the convergence of a forward-backward splitting method that alternates between steps on a fine and a coarse grid. Our focus is a total variation regularised inverse imaging problems, specifically, their dual problems, for which we develop in detail the relevant coarse-grid problems. We demonstrate the performance of our method on total variation denoising and magnetic resonance imaging.

math.OC↗