{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:DXOFH4IYAQ7OGKDI5KCIY7AGP4","short_pith_number":"pith:DXOFH4IY","schema_version":"1.0","canonical_sha256":"1ddc53f118043ee32868ea848c7c067f18628f52da05ea341e3b851bb67343b8","source":{"kind":"arxiv","id":"1902.01572","version":1},"attestation_state":"computed","paper":{"title":"Advances in Low-Memory Subgradient Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexander Gasnikov, Evgeni Nurminsky, Fedor Stonyakin, Pavel Dvurechensky","submitted_at":"2019-02-05T07:28:53Z","abstract_excerpt":"This chapter is devoted to the black-box subgradient algorithms with the minimal requirements for the storage of auxiliary results, which are necessary to execute these algorithms. It starts with the original result of N.Z. Shor which open this field with the application to the classical transportation problem. To discuss the fundamentals of non-smooth optimization the theoretical complexity bounds for smooth and non-smooth convex and quasi-convex optimization problems are briefly exposed with the special attention given to adaptive step-size policy. Than this chapter contains descriptions of "},"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":"1902.01572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-05T07:28:53Z","cross_cats_sorted":[],"title_canon_sha256":"c67c987aa824cb94afb1549e5299ef239db24f780d05dc4f24aa16999067ab5a","abstract_canon_sha256":"65527a541436f43bdb543818a4514131b466429f64380f6387709aa15c5cdd53"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:47.266397Z","signature_b64":"SykLj/dge3lI47n3+kV1uA8BaG9nrCpLwP4wEnF0QVwBdUrnKVHUqF1+NFH0SlZZJW6LeHe8zPGQTan/xBWBAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ddc53f118043ee32868ea848c7c067f18628f52da05ea341e3b851bb67343b8","last_reissued_at":"2026-05-17T23:54:47.265878Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:47.265878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Advances in Low-Memory Subgradient Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexander Gasnikov, Evgeni Nurminsky, Fedor Stonyakin, Pavel Dvurechensky","submitted_at":"2019-02-05T07:28:53Z","abstract_excerpt":"This chapter is devoted to the black-box subgradient algorithms with the minimal requirements for the storage of auxiliary results, which are necessary to execute these algorithms. It starts with the original result of N.Z. Shor which open this field with the application to the classical transportation problem. To discuss the fundamentals of non-smooth optimization the theoretical complexity bounds for smooth and non-smooth convex and quasi-convex optimization problems are briefly exposed with the special attention given to adaptive step-size policy. Than this chapter contains descriptions of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01572","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":""},"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":"1902.01572","created_at":"2026-05-17T23:54:47.265971+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.01572v1","created_at":"2026-05-17T23:54:47.265971+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01572","created_at":"2026-05-17T23:54:47.265971+00:00"},{"alias_kind":"pith_short_12","alias_value":"DXOFH4IYAQ7O","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"DXOFH4IYAQ7OGKDI","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"DXOFH4IY","created_at":"2026-05-18T12:33:15.570797+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/DXOFH4IYAQ7OGKDI5KCIY7AGP4","json":"https://pith.science/pith/DXOFH4IYAQ7OGKDI5KCIY7AGP4.json","graph_json":"https://pith.science/api/pith-number/DXOFH4IYAQ7OGKDI5KCIY7AGP4/graph.json","events_json":"https://pith.science/api/pith-number/DXOFH4IYAQ7OGKDI5KCIY7AGP4/events.json","paper":"https://pith.science/paper/DXOFH4IY"},"agent_actions":{"view_html":"https://pith.science/pith/DXOFH4IYAQ7OGKDI5KCIY7AGP4","download_json":"https://pith.science/pith/DXOFH4IYAQ7OGKDI5KCIY7AGP4.json","view_paper":"https://pith.science/paper/DXOFH4IY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.01572&json=true","fetch_graph":"https://pith.science/api/pith-number/DXOFH4IYAQ7OGKDI5KCIY7AGP4/graph.json","fetch_events":"https://pith.science/api/pith-number/DXOFH4IYAQ7OGKDI5KCIY7AGP4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DXOFH4IYAQ7OGKDI5KCIY7AGP4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DXOFH4IYAQ7OGKDI5KCIY7AGP4/action/storage_attestation","attest_author":"https://pith.science/pith/DXOFH4IYAQ7OGKDI5KCIY7AGP4/action/author_attestation","sign_citation":"https://pith.science/pith/DXOFH4IYAQ7OGKDI5KCIY7AGP4/action/citation_signature","submit_replication":"https://pith.science/pith/DXOFH4IYAQ7OGKDI5KCIY7AGP4/action/replication_record"}},"created_at":"2026-05-17T23:54:47.265971+00:00","updated_at":"2026-05-17T23:54:47.265971+00:00"}