{"paper":{"title":"Global optimization of quadratic root-difference minimization under elliptic annulus constraints","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Meijia Yang, Yong Xia","submitted_at":"2026-05-28T03:21:39Z","abstract_excerpt":"This paper studies the nonconvex quadratic root-difference minimization under elliptic annulus constraints {\\rm (QR)}. We first establish the Annulus Brickman theorem and equivalently reformulate {\\rm (QR)} as a 2-dimensional convex problem {\\rm (HP)} with hidden variables. We employ the Frank-Wolfe algorithm to globally solve {\\rm (HP)}. A key finding is that the solutions of the Frank-Wolfe subproblems, which are traditionally viewed as mere auxiliary updates, are proven to be $O(1/\\sqrt{k})$-approximate solutions of the original problem {\\rm (QR)}. This transforms an algorithmic by-product "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29294","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.29294/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}