{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:MLPIR575GFMAPZGXNE2OODJSII","short_pith_number":"pith:MLPIR575","schema_version":"1.0","canonical_sha256":"62de88f7fd315807e4d76934e70d32422dc988e0555f0a63bc8d0e6b845a4e6a","source":{"kind":"arxiv","id":"1008.5231","version":3},"attestation_state":"computed","paper":{"title":"The adaptive projected subgradient method constrained by families of quasi-nonexpansive mappings and its application to online learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"math.OC","authors_text":"Isao Yamada, Konstantinos Slavakis","submitted_at":"2010-08-31T07:07:27Z","abstract_excerpt":"Many online, i.e., time-adaptive, inverse problems in signal processing and machine learning fall under the wide umbrella of the asymptotic minimization of a sequence of non-negative, convex, and continuous functions. To incorporate a-priori knowledge into the design, the asymptotic minimization task is usually constrained on a fixed closed convex set, which is dictated by the available a-priori information. To increase versatility towards the usage of the available information, the present manuscript extends the Adaptive Projected Subgradient Method (APSM) by introducing an algorithmic scheme"},"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":"1008.5231","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-08-31T07:07:27Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"title_canon_sha256":"72a367ea90ebd1f10b34c83ba89b0698f7c96cb25576cc390e8b58072f469113","abstract_canon_sha256":"58fcd108610596d082ba5545ac3396b1bcd20b0ddfee012c35840a4f432b9913"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:12.155403Z","signature_b64":"Xbww/tFSIUSkirnYjzppGq/Dn6BVpdXvV/+d3JSt4OhXWjBa4vu0vqbuT69v9pqa8voWZ0pI/LB98ML+j02ICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62de88f7fd315807e4d76934e70d32422dc988e0555f0a63bc8d0e6b845a4e6a","last_reissued_at":"2026-05-18T04:16:12.154997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:12.154997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The adaptive projected subgradient method constrained by families of quasi-nonexpansive mappings and its application to online learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"math.OC","authors_text":"Isao Yamada, Konstantinos Slavakis","submitted_at":"2010-08-31T07:07:27Z","abstract_excerpt":"Many online, i.e., time-adaptive, inverse problems in signal processing and machine learning fall under the wide umbrella of the asymptotic minimization of a sequence of non-negative, convex, and continuous functions. To incorporate a-priori knowledge into the design, the asymptotic minimization task is usually constrained on a fixed closed convex set, which is dictated by the available a-priori information. To increase versatility towards the usage of the available information, the present manuscript extends the Adaptive Projected Subgradient Method (APSM) by introducing an algorithmic scheme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.5231","kind":"arxiv","version":3},"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":"1008.5231","created_at":"2026-05-18T04:16:12.155056+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.5231v3","created_at":"2026-05-18T04:16:12.155056+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.5231","created_at":"2026-05-18T04:16:12.155056+00:00"},{"alias_kind":"pith_short_12","alias_value":"MLPIR575GFMA","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"MLPIR575GFMAPZGX","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"MLPIR575","created_at":"2026-05-18T12:26:10.704358+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/MLPIR575GFMAPZGXNE2OODJSII","json":"https://pith.science/pith/MLPIR575GFMAPZGXNE2OODJSII.json","graph_json":"https://pith.science/api/pith-number/MLPIR575GFMAPZGXNE2OODJSII/graph.json","events_json":"https://pith.science/api/pith-number/MLPIR575GFMAPZGXNE2OODJSII/events.json","paper":"https://pith.science/paper/MLPIR575"},"agent_actions":{"view_html":"https://pith.science/pith/MLPIR575GFMAPZGXNE2OODJSII","download_json":"https://pith.science/pith/MLPIR575GFMAPZGXNE2OODJSII.json","view_paper":"https://pith.science/paper/MLPIR575","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.5231&json=true","fetch_graph":"https://pith.science/api/pith-number/MLPIR575GFMAPZGXNE2OODJSII/graph.json","fetch_events":"https://pith.science/api/pith-number/MLPIR575GFMAPZGXNE2OODJSII/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MLPIR575GFMAPZGXNE2OODJSII/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MLPIR575GFMAPZGXNE2OODJSII/action/storage_attestation","attest_author":"https://pith.science/pith/MLPIR575GFMAPZGXNE2OODJSII/action/author_attestation","sign_citation":"https://pith.science/pith/MLPIR575GFMAPZGXNE2OODJSII/action/citation_signature","submit_replication":"https://pith.science/pith/MLPIR575GFMAPZGXNE2OODJSII/action/replication_record"}},"created_at":"2026-05-18T04:16:12.155056+00:00","updated_at":"2026-05-18T04:16:12.155056+00:00"}