{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BFXUR6Y3ZBYZQHBOT6KOG2I54Z","short_pith_number":"pith:BFXUR6Y3","schema_version":"1.0","canonical_sha256":"096f48fb1bc871981c2e9f94e3691de67ac9e755d4f20d0f7ebb89c5399e3019","source":{"kind":"arxiv","id":"1906.02608","version":2},"attestation_state":"computed","paper":{"title":"Hamiltonian descent for composite objectives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Brendan O'Donoghue, Chris J. Maddison","submitted_at":"2019-06-06T14:17:04Z","abstract_excerpt":"In optimization the duality gap between the primal and the dual problems is a measure of the suboptimality of any primal-dual point. In classical mechanics the equations of motion of a system can be derived from the Hamiltonian function, which is a quantity that describes the total energy of the system. In this paper we consider a convex optimization problem consisting of the sum of two convex functions, sometimes referred to as a composite objective, and we identify the duality gap to be the 'energy' of the system. In the Hamiltonian formalism the energy is conserved, so we add a contractive "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1906.02608","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-06T14:17:04Z","cross_cats_sorted":[],"title_canon_sha256":"95ef2281df765f95a4c9d393e226250cc9f2923e527ad50470f6ac793eb55401","abstract_canon_sha256":"eebced0e1d397a1594f6b90607d96cd11e06a2dcacc84f3bf8016850be800e9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:19:36.788755Z","signature_b64":"FxdfeAapd5OG/G41Reqe46PCJdcf65tKZC502KDfYZq2/HAqMdgR1zoNB9Slva2R3/Ts2zEAg+Y/5/14Y2FCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"096f48fb1bc871981c2e9f94e3691de67ac9e755d4f20d0f7ebb89c5399e3019","last_reissued_at":"2026-07-05T00:19:36.788250Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:19:36.788250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hamiltonian descent for composite objectives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Brendan O'Donoghue, Chris J. Maddison","submitted_at":"2019-06-06T14:17:04Z","abstract_excerpt":"In optimization the duality gap between the primal and the dual problems is a measure of the suboptimality of any primal-dual point. In classical mechanics the equations of motion of a system can be derived from the Hamiltonian function, which is a quantity that describes the total energy of the system. In this paper we consider a convex optimization problem consisting of the sum of two convex functions, sometimes referred to as a composite objective, and we identify the duality gap to be the 'energy' of the system. In the Hamiltonian formalism the energy is conserved, so we add a contractive "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.02608","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/1906.02608/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1906.02608","created_at":"2026-07-05T00:19:36.788309+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.02608v2","created_at":"2026-07-05T00:19:36.788309+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.02608","created_at":"2026-07-05T00:19:36.788309+00:00"},{"alias_kind":"pith_short_12","alias_value":"BFXUR6Y3ZBYZ","created_at":"2026-07-05T00:19:36.788309+00:00"},{"alias_kind":"pith_short_16","alias_value":"BFXUR6Y3ZBYZQHBO","created_at":"2026-07-05T00:19:36.788309+00:00"},{"alias_kind":"pith_short_8","alias_value":"BFXUR6Y3","created_at":"2026-07-05T00:19:36.788309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BFXUR6Y3ZBYZQHBOT6KOG2I54Z","json":"https://pith.science/pith/BFXUR6Y3ZBYZQHBOT6KOG2I54Z.json","graph_json":"https://pith.science/api/pith-number/BFXUR6Y3ZBYZQHBOT6KOG2I54Z/graph.json","events_json":"https://pith.science/api/pith-number/BFXUR6Y3ZBYZQHBOT6KOG2I54Z/events.json","paper":"https://pith.science/paper/BFXUR6Y3"},"agent_actions":{"view_html":"https://pith.science/pith/BFXUR6Y3ZBYZQHBOT6KOG2I54Z","download_json":"https://pith.science/pith/BFXUR6Y3ZBYZQHBOT6KOG2I54Z.json","view_paper":"https://pith.science/paper/BFXUR6Y3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.02608&json=true","fetch_graph":"https://pith.science/api/pith-number/BFXUR6Y3ZBYZQHBOT6KOG2I54Z/graph.json","fetch_events":"https://pith.science/api/pith-number/BFXUR6Y3ZBYZQHBOT6KOG2I54Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BFXUR6Y3ZBYZQHBOT6KOG2I54Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BFXUR6Y3ZBYZQHBOT6KOG2I54Z/action/storage_attestation","attest_author":"https://pith.science/pith/BFXUR6Y3ZBYZQHBOT6KOG2I54Z/action/author_attestation","sign_citation":"https://pith.science/pith/BFXUR6Y3ZBYZQHBOT6KOG2I54Z/action/citation_signature","submit_replication":"https://pith.science/pith/BFXUR6Y3ZBYZQHBOT6KOG2I54Z/action/replication_record"}},"created_at":"2026-07-05T00:19:36.788309+00:00","updated_at":"2026-07-05T00:19:36.788309+00:00"}