{"paper":{"title":"Revisiting several problems and algorithms in continuous location with $\\ell_p$ norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.OC","authors_text":"Justo Puerto, Safae El Haj Ben Ali, V\\'ictor Blanco","submitted_at":"2013-12-28T21:08:09Z","abstract_excerpt":"This paper addresses the general continuous single facility location problems in finite dimension spaces under possibly different $\\ell_p$ norms in the demand points. We analyze the difficulty of this family of problems and revisit convergence properties of some well-known algorithms. The ultimate goal is to provide a common approach to solve the family of continuous $\\ell_p$ ordered median location problems in dimension $d$ (including of course the $\\ell_p$ minisum or Fermat-Weber location problem for any $p\\ge 1$). We prove that this approach has a polynomial worse case complexity for monoto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7473","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}