{"paper":{"title":"Tight Lower Bounds for Binary First-Order Oracles for Convex Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Amitabh Basu, Marco Molinaro, Phillip Kerger","submitted_at":"2025-11-03T21:42:30Z","abstract_excerpt":"We establish new lower-bounds for the information complexity of mixed-integer convex optimization under two \"bit-wise\" oracles.\n  The first oracle provides bits of first-order information in the standard\n  coordinate model, and the second oracle answers whether the inner product of a specified vector with the gradient of the function at a point or\n  the normal vector of a separating hyperplane for the feasible region is\n  positive or non-positive, thus also providing one bit of first-order information. The new contribution is that under such oracles, the complexity is quadratic in the number o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.02082","kind":"arxiv","version":2},"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/2511.02082/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"}