5 papers
Riemannian Multilevel Optimization with Application to Constrained Energy Minimization Problems
Yara Elshiaty, Stefania Petra, Jonas Püschel +2
Multilevel optimization methods are highly effective for discretized energy minimization problems, but their Euclidean formulation does not directly apply to manifold constraints.…
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…
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…
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…
Accelerated Bregmann divergence optimization with SMART: an information geometry point of view
Maren Raus, Yara Elshiaty, Stefania Petra
We investigate the problem of minimizing Kullback-Leibler divergence between a linear model and a positive vector in different convex domains (positive orthant, -dimens…