{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MDQ6QOCSWJPYLBVRKSNSIEJXEN","short_pith_number":"pith:MDQ6QOCS","schema_version":"1.0","canonical_sha256":"60e1e83852b25f8586b1549b241137237a75c9a911b8ce2fdf5e3ddc7fc82968","source":{"kind":"arxiv","id":"2608.04884","version":1},"attestation_state":"computed","paper":{"title":"A Few Accelerated Algorithms for Convex Optimization under $(H_0,H_1)$-Smoothness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Aleksandr Lobanov","submitted_at":"2026-08-05T14:09:13Z","abstract_excerpt":"We develop accelerated algorithms for convex $(H_0,H_1)$-smooth optimization, where $\\|\\nabla^2 f(x)\\|\\le H_0+H_1(f(x)-f^*)$. This class generalizes standard smoothness and contains the $(L_0,L_1)$-smooth class. Combining a Nesterov-type accelerated gradient scheme with small-dimensional relaxation and phase restarts, we obtain a full-gradient method with iteration complexity $\\widetilde O(\\sqrt{H_0\\widetilde R^2/\\varepsilon}+\\sqrt{H_1\\widetilde R^2}\\log(F_0/\\varepsilon))$. We extend the same approach to randomized coordinate optimization, obtaining a coordinate method with uniform sampling wh"},"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":"2608.04884","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-08-05T14:09:13Z","cross_cats_sorted":[],"title_canon_sha256":"0023b6acf4d10b273cc29d01681112f9111353eaca1ce1fd6a3d0c5017b6207e","abstract_canon_sha256":"ebf7488f7bfadd3853cbc60e84d1b8bee7368dcb9d78f5186524c07e54b685d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:47:27.333273Z","signature_b64":"aD9kqqR9nlxEFXkv+PwTzw/LRfXGhof1JcoBAOP3ehUI3QONQLyaqjF5SGW91r1FNOTwrMtScOiwMJGHyD0RDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60e1e83852b25f8586b1549b241137237a75c9a911b8ce2fdf5e3ddc7fc82968","last_reissued_at":"2026-08-06T01:47:27.331823Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:47:27.331823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Few Accelerated Algorithms for Convex Optimization under $(H_0,H_1)$-Smoothness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Aleksandr Lobanov","submitted_at":"2026-08-05T14:09:13Z","abstract_excerpt":"We develop accelerated algorithms for convex $(H_0,H_1)$-smooth optimization, where $\\|\\nabla^2 f(x)\\|\\le H_0+H_1(f(x)-f^*)$. This class generalizes standard smoothness and contains the $(L_0,L_1)$-smooth class. Combining a Nesterov-type accelerated gradient scheme with small-dimensional relaxation and phase restarts, we obtain a full-gradient method with iteration complexity $\\widetilde O(\\sqrt{H_0\\widetilde R^2/\\varepsilon}+\\sqrt{H_1\\widetilde R^2}\\log(F_0/\\varepsilon))$. We extend the same approach to randomized coordinate optimization, obtaining a coordinate method with uniform sampling wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04884","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/2608.04884/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":"2608.04884","created_at":"2026-08-06T01:47:27.333704+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.04884v1","created_at":"2026-08-06T01:47:27.333704+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04884","created_at":"2026-08-06T01:47:27.333704+00:00"},{"alias_kind":"pith_short_12","alias_value":"MDQ6QOCSWJPY","created_at":"2026-08-06T01:47:27.333704+00:00"},{"alias_kind":"pith_short_16","alias_value":"MDQ6QOCSWJPYLBVR","created_at":"2026-08-06T01:47:27.333704+00:00"},{"alias_kind":"pith_short_8","alias_value":"MDQ6QOCS","created_at":"2026-08-06T01:47:27.333704+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/MDQ6QOCSWJPYLBVRKSNSIEJXEN","json":"https://pith.science/pith/MDQ6QOCSWJPYLBVRKSNSIEJXEN.json","graph_json":"https://pith.science/api/pith-number/MDQ6QOCSWJPYLBVRKSNSIEJXEN/graph.json","events_json":"https://pith.science/api/pith-number/MDQ6QOCSWJPYLBVRKSNSIEJXEN/events.json","paper":"https://pith.science/paper/MDQ6QOCS"},"agent_actions":{"view_html":"https://pith.science/pith/MDQ6QOCSWJPYLBVRKSNSIEJXEN","download_json":"https://pith.science/pith/MDQ6QOCSWJPYLBVRKSNSIEJXEN.json","view_paper":"https://pith.science/paper/MDQ6QOCS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.04884&json=true","fetch_graph":"https://pith.science/api/pith-number/MDQ6QOCSWJPYLBVRKSNSIEJXEN/graph.json","fetch_events":"https://pith.science/api/pith-number/MDQ6QOCSWJPYLBVRKSNSIEJXEN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MDQ6QOCSWJPYLBVRKSNSIEJXEN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MDQ6QOCSWJPYLBVRKSNSIEJXEN/action/storage_attestation","attest_author":"https://pith.science/pith/MDQ6QOCSWJPYLBVRKSNSIEJXEN/action/author_attestation","sign_citation":"https://pith.science/pith/MDQ6QOCSWJPYLBVRKSNSIEJXEN/action/citation_signature","submit_replication":"https://pith.science/pith/MDQ6QOCSWJPYLBVRKSNSIEJXEN/action/replication_record"}},"created_at":"2026-08-06T01:47:27.333704+00:00","updated_at":"2026-08-06T01:47:27.333704+00:00"}