{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:ZAW3YU34WBFU3AC57VB23FUQJI","short_pith_number":"pith:ZAW3YU34","schema_version":"1.0","canonical_sha256":"c82dbc537cb04b4d805dfd43ad96904a057d37c1639ad345359da574669ebf0d","source":{"kind":"arxiv","id":"2403.06930","version":2},"attestation_state":"computed","paper":{"title":"Heavy Ball Momentum for Non-Strongly Convex Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Aude Rondepierre, Charles Dossal, Hippolyte Labarri\\`ere, Jean-Fran\\c{c}ois Aujol","submitted_at":"2024-03-11T17:17:18Z","abstract_excerpt":"When considering the minimization of a quadratic or strongly convex function, it is well known that first-order methods involving an inertial term weighted by a constant-in-time parameter are particularly efficient (see Polyak [32], Nesterov [28], and references therein). By setting the inertial parameter according to the condition number of the objective function, these methods guarantee a fast exponential decay of the error. We prove that this type of schemes (which are later called Heavy Ball schemes) is relevant in a relaxed setting, i.e. for composite functions satisfying a quadratic grow"},"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":"2403.06930","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-03-11T17:17:18Z","cross_cats_sorted":[],"title_canon_sha256":"df7dbf3c313cb507ddf3761c228bb78e6f6fb93aa003581019a78005a33b9e0a","abstract_canon_sha256":"3fcc0ba2c97f0fd67e84e9a4ea0866ada9571b3dd590dc0f3871aeef17e31bda"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:01:32.501231Z","signature_b64":"pFdYXonK/ir7fFIJjo6uY9kPFO5+3T2yki/GkaMGOsm17UBFQ/Hxtr+qhNfYYeMkNMMypTGx08KWkivEo/emDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c82dbc537cb04b4d805dfd43ad96904a057d37c1639ad345359da574669ebf0d","last_reissued_at":"2026-07-05T10:01:32.500832Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:01:32.500832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heavy Ball Momentum for Non-Strongly Convex Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Aude Rondepierre, Charles Dossal, Hippolyte Labarri\\`ere, Jean-Fran\\c{c}ois Aujol","submitted_at":"2024-03-11T17:17:18Z","abstract_excerpt":"When considering the minimization of a quadratic or strongly convex function, it is well known that first-order methods involving an inertial term weighted by a constant-in-time parameter are particularly efficient (see Polyak [32], Nesterov [28], and references therein). By setting the inertial parameter according to the condition number of the objective function, these methods guarantee a fast exponential decay of the error. We prove that this type of schemes (which are later called Heavy Ball schemes) is relevant in a relaxed setting, i.e. for composite functions satisfying a quadratic grow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.06930","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/2403.06930/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":"2403.06930","created_at":"2026-07-05T10:01:32.500890+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.06930v2","created_at":"2026-07-05T10:01:32.500890+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.06930","created_at":"2026-07-05T10:01:32.500890+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZAW3YU34WBFU","created_at":"2026-07-05T10:01:32.500890+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZAW3YU34WBFU3AC5","created_at":"2026-07-05T10:01:32.500890+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZAW3YU34","created_at":"2026-07-05T10:01:32.500890+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.11705","citing_title":"Heavy-ball dynamics with Hessian-driven damping for non-convex optimization under the {\\L}ojasiewicz condition","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZAW3YU34WBFU3AC57VB23FUQJI","json":"https://pith.science/pith/ZAW3YU34WBFU3AC57VB23FUQJI.json","graph_json":"https://pith.science/api/pith-number/ZAW3YU34WBFU3AC57VB23FUQJI/graph.json","events_json":"https://pith.science/api/pith-number/ZAW3YU34WBFU3AC57VB23FUQJI/events.json","paper":"https://pith.science/paper/ZAW3YU34"},"agent_actions":{"view_html":"https://pith.science/pith/ZAW3YU34WBFU3AC57VB23FUQJI","download_json":"https://pith.science/pith/ZAW3YU34WBFU3AC57VB23FUQJI.json","view_paper":"https://pith.science/paper/ZAW3YU34","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.06930&json=true","fetch_graph":"https://pith.science/api/pith-number/ZAW3YU34WBFU3AC57VB23FUQJI/graph.json","fetch_events":"https://pith.science/api/pith-number/ZAW3YU34WBFU3AC57VB23FUQJI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZAW3YU34WBFU3AC57VB23FUQJI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZAW3YU34WBFU3AC57VB23FUQJI/action/storage_attestation","attest_author":"https://pith.science/pith/ZAW3YU34WBFU3AC57VB23FUQJI/action/author_attestation","sign_citation":"https://pith.science/pith/ZAW3YU34WBFU3AC57VB23FUQJI/action/citation_signature","submit_replication":"https://pith.science/pith/ZAW3YU34WBFU3AC57VB23FUQJI/action/replication_record"}},"created_at":"2026-07-05T10:01:32.500890+00:00","updated_at":"2026-07-05T10:01:32.500890+00:00"}