Multilevel Bregman Proximal Gradient Descent
Abstract
Abstract. We present the Multilevel Bregman Proximal Gradient Descent (ML-BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipschitz smoothness. Our approach extends the classical multilevel optimization framework (MGOPT) to Bregman-based geometries and constrained domains. We provide a rigorous analysis of ML-BPGD for multiple levels and establish well-posedness together with a global linear convergence rate. We demonstrate the effectiveness of ML-BPGD in the context of image reconstruction and validate its performance through numerical experiments.
Fields of Study & Subjects
Stochastic Gradient Optimization Techniques
Sparse and Compressive Sensing Techniques
Optimization and Variational Analysis
Publication details
- Journal / source
- SIAM Journal on Imaging Sciences
- Volume
- 19
- Issue
- 2
- Pages
- 913–942
- Publication date
- 5 May 2026
- Language
- EN