Non-Archimedean Polydisc Spaces and Applications to Optimisation
Researchers have introduced a novel optimization framework utilizing non-Archimedean polydisc spaces, inspired by Berkovich geometry. These spaces, formed by products of closed balls over non-Archimedean fields, offer a blend of hierarchical structure and geometric properties suitable for optimization. The work includes theoretical developments on geodesic uniqueness and the approximation properties of specific function classes, alongside an open-source Julia library for implementing these optimization procedures. AI