Convex optimization on CAT(0) cubical complexes
Optimization and Control
2024-05-06 v1
Abstract
We consider geodesically convex optimization problems involving distances to a finite set of points in a CAT(0) cubical complex. Examples include the minimum enclosing ball problem, the weighted mean and median problems, and the feasibility and projection problems for intersecting balls with centers in . We propose a decomposition approach relying on standard Euclidean cutting plane algorithms. The cutting planes are readily derivable from efficient algorithms for computing geodesics in the complex.
Cite
@article{arxiv.2405.01968,
title = {Convex optimization on CAT(0) cubical complexes},
author = {Ariel Goodwin and Adrian S. Lewis and Genaro Lopez-Acedo and Adriana Nicolae},
journal= {arXiv preprint arXiv:2405.01968},
year = {2024}
}