Multilevel Geometric Optimization for Regularised Constrained Linear Inverse Problems

• URL: http://arxiv.org/abs/2207.04934v3
• Date: Mon, 22 Apr 2024 14:11:18 GMT
• Title: Multilevel Geometric Optimization for Regularised Constrained Linear Inverse Problems
• Authors: Sebastian Müller, Stefania Petra, Matthias Zisler,
• Abstract summary: We consider a hierarchy of models with varying discretization levels. Finer models are accurate but expensive to compute, while coarser models are less accurate but cheaper to compute. When working at the fine level, multilevel optimisation computes the search direction based on a coarser model which speeds up updates at the fine level.
• Score: 3.3161769688599025
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are accurate but expensive to compute, while coarser models are less accurate but cheaper to compute. When working at the fine level, multilevel optimisation computes the search direction based on a coarser model which speeds up updates at the fine level. Moreover, exploiting geometry induced by the hierarchy the feasibility of the updates is preserved. In particular, our approach extends classical components of multigrid methods like restriction and prolongation to the Riemannian structure of our constraints.

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