{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:CUYD4W3MA5IA4YP5QQJVSDPGQJ","short_pith_number":"pith:CUYD4W3M","canonical_record":{"source":{"id":"2002.11582","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-02-26T16:06:27Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"1c9177199c58f5617f8cb4062329d78f520afde482a658b1e6fb373f4bbcf863","abstract_canon_sha256":"5783ad74a7ff7882e11490ebc4092d4fa5891e8f6e9bcc8b54b1facb5897ca76"},"schema_version":"1.0"},"canonical_sha256":"15303e5b6c07500e61fd8413590de68268eb77f49969590c09cdde4c79a7de03","source":{"kind":"arxiv","id":"2002.11582","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.11582","created_at":"2026-07-05T00:58:24Z"},{"alias_kind":"arxiv_version","alias_value":"2002.11582v3","created_at":"2026-07-05T00:58:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.11582","created_at":"2026-07-05T00:58:24Z"},{"alias_kind":"pith_short_12","alias_value":"CUYD4W3MA5IA","created_at":"2026-07-05T00:58:24Z"},{"alias_kind":"pith_short_16","alias_value":"CUYD4W3MA5IA4YP5","created_at":"2026-07-05T00:58:24Z"},{"alias_kind":"pith_short_8","alias_value":"CUYD4W3M","created_at":"2026-07-05T00:58:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:CUYD4W3MA5IA4YP5QQJVSDPGQJ","target":"record","payload":{"canonical_record":{"source":{"id":"2002.11582","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-02-26T16:06:27Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"1c9177199c58f5617f8cb4062329d78f520afde482a658b1e6fb373f4bbcf863","abstract_canon_sha256":"5783ad74a7ff7882e11490ebc4092d4fa5891e8f6e9bcc8b54b1facb5897ca76"},"schema_version":"1.0"},"canonical_sha256":"15303e5b6c07500e61fd8413590de68268eb77f49969590c09cdde4c79a7de03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:58:24.592356Z","signature_b64":"dqd0FmxlXkiynx56IxdXjmQYy8rSQgTe7RXhQPAKuh1FG/gMEeOxN1eh2Kaps9VIjowRCYX54daXSsKY0TkXCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15303e5b6c07500e61fd8413590de68268eb77f49969590c09cdde4c79a7de03","last_reissued_at":"2026-07-05T00:58:24.591878Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:58:24.591878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.11582","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:58:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"88bZShK5EF+hhmScxLFmMJUMhx2ho9gsummTVjn3BX5tVhSnC5D1QgtYyLV13h3nmHY6TS17Rn/+foNWS+6ODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T03:57:33.900843Z"},"content_sha256":"68ba4788c3a2403174c9f083f3822a338092dd9265f3420e216b239781fef2cc","schema_version":"1.0","event_id":"sha256:68ba4788c3a2403174c9f083f3822a338092dd9265f3420e216b239781fef2cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:CUYD4W3MA5IA4YP5QQJVSDPGQJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proximal Gradient Algorithm with Momentum and Flexible Parameter Restart for Nonconvex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Kaiyi Ji, Vahid Tarokh, Yingbin Liang, Yi Zhou, Zhe Wang","submitted_at":"2020-02-26T16:06:27Z","abstract_excerpt":"Various types of parameter restart schemes have been proposed for accelerated gradient algorithms to facilitate their practical convergence in convex optimization. However, the convergence properties of accelerated gradient algorithms under parameter restart remain obscure in nonconvex optimization. In this paper, we propose a novel accelerated proximal gradient algorithm with parameter restart (named APG-restart) for solving nonconvex and nonsmooth problems. Our APG-restart is designed to 1) allow for adopting flexible parameter restart schemes that cover many existing ones; 2) have a global "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.11582","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.11582/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:58:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0WRflDe+EkwwMj/OS4rHk0FQaBXQHZFvlbJlsGpMEWGTEBfwI70jXvyafzsJtTECDHW+JGk+ZmCZAH8sf2DGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T03:57:33.901317Z"},"content_sha256":"cb66ba57da3da648d2d6b188d59f672f4a18080b3188c6a2d0e8a3f856058217","schema_version":"1.0","event_id":"sha256:cb66ba57da3da648d2d6b188d59f672f4a18080b3188c6a2d0e8a3f856058217"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CUYD4W3MA5IA4YP5QQJVSDPGQJ/bundle.json","state_url":"https://pith.science/pith/CUYD4W3MA5IA4YP5QQJVSDPGQJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CUYD4W3MA5IA4YP5QQJVSDPGQJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T03:57:33Z","links":{"resolver":"https://pith.science/pith/CUYD4W3MA5IA4YP5QQJVSDPGQJ","bundle":"https://pith.science/pith/CUYD4W3MA5IA4YP5QQJVSDPGQJ/bundle.json","state":"https://pith.science/pith/CUYD4W3MA5IA4YP5QQJVSDPGQJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CUYD4W3MA5IA4YP5QQJVSDPGQJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:CUYD4W3MA5IA4YP5QQJVSDPGQJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5783ad74a7ff7882e11490ebc4092d4fa5891e8f6e9bcc8b54b1facb5897ca76","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-02-26T16:06:27Z","title_canon_sha256":"1c9177199c58f5617f8cb4062329d78f520afde482a658b1e6fb373f4bbcf863"},"schema_version":"1.0","source":{"id":"2002.11582","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.11582","created_at":"2026-07-05T00:58:24Z"},{"alias_kind":"arxiv_version","alias_value":"2002.11582v3","created_at":"2026-07-05T00:58:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.11582","created_at":"2026-07-05T00:58:24Z"},{"alias_kind":"pith_short_12","alias_value":"CUYD4W3MA5IA","created_at":"2026-07-05T00:58:24Z"},{"alias_kind":"pith_short_16","alias_value":"CUYD4W3MA5IA4YP5","created_at":"2026-07-05T00:58:24Z"},{"alias_kind":"pith_short_8","alias_value":"CUYD4W3M","created_at":"2026-07-05T00:58:24Z"}],"graph_snapshots":[{"event_id":"sha256:cb66ba57da3da648d2d6b188d59f672f4a18080b3188c6a2d0e8a3f856058217","target":"graph","created_at":"2026-07-05T00:58:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2002.11582/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Various types of parameter restart schemes have been proposed for accelerated gradient algorithms to facilitate their practical convergence in convex optimization. However, the convergence properties of accelerated gradient algorithms under parameter restart remain obscure in nonconvex optimization. In this paper, we propose a novel accelerated proximal gradient algorithm with parameter restart (named APG-restart) for solving nonconvex and nonsmooth problems. Our APG-restart is designed to 1) allow for adopting flexible parameter restart schemes that cover many existing ones; 2) have a global ","authors_text":"Kaiyi Ji, Vahid Tarokh, Yingbin Liang, Yi Zhou, Zhe Wang","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-02-26T16:06:27Z","title":"Proximal Gradient Algorithm with Momentum and Flexible Parameter Restart for Nonconvex Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.11582","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:68ba4788c3a2403174c9f083f3822a338092dd9265f3420e216b239781fef2cc","target":"record","created_at":"2026-07-05T00:58:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5783ad74a7ff7882e11490ebc4092d4fa5891e8f6e9bcc8b54b1facb5897ca76","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-02-26T16:06:27Z","title_canon_sha256":"1c9177199c58f5617f8cb4062329d78f520afde482a658b1e6fb373f4bbcf863"},"schema_version":"1.0","source":{"id":"2002.11582","kind":"arxiv","version":3}},"canonical_sha256":"15303e5b6c07500e61fd8413590de68268eb77f49969590c09cdde4c79a7de03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15303e5b6c07500e61fd8413590de68268eb77f49969590c09cdde4c79a7de03","first_computed_at":"2026-07-05T00:58:24.591878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:58:24.591878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dqd0FmxlXkiynx56IxdXjmQYy8rSQgTe7RXhQPAKuh1FG/gMEeOxN1eh2Kaps9VIjowRCYX54daXSsKY0TkXCA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:58:24.592356Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.11582","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68ba4788c3a2403174c9f083f3822a338092dd9265f3420e216b239781fef2cc","sha256:cb66ba57da3da648d2d6b188d59f672f4a18080b3188c6a2d0e8a3f856058217"],"state_sha256":"5f0c24a673d738a45a26b20f2146f0f90ebb584380c40aa73e8d6ce9dca27910"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ah5N5auPft1tG71exohZuVwI4RmyHGTHnsu4DJUlqyd0eVZHsS3CrULph15lEMXavZYE16xUfkjto+4lyibwBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T03:57:33.906131Z","bundle_sha256":"fa8ad116fa2688e933d0676170a4ec7309c0a98ab4b11bce387659d2a4102e00"}}