English

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 AA 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 AA. 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.

Keywords

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}
}
R2 v1 2026-06-28T16:15:19.846Z