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math.OC2025
Multilevel Bregman Proximal Gradient Descent
Yara Elshiaty, Stefania Petra
We present the Multilevel Bregman Proximal Gradient Descent (ML BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipsch…
math.OC2025
Multilevel Optimization: Geometric Coarse Models and Convergence Analysis
Ferdinand Vanmaele, Yara Elshiaty, Stefania Petra
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model t…
math.OC2025
Information Geometry of Exponentiated Gradient: Convergence beyond L-Smoothness
Yara Elshiaty, Ferdinand Vanmaele, Stefania Petra
We study the minimization of smooth, possibly nonconvex functions over the positive orthant, a key setting in Poisson inverse problems, using the exponentiated gradient (EG) method…