{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:5DC5VUBYPEADPFPHX64JUEANOZ","short_pith_number":"pith:5DC5VUBY","canonical_record":{"source":{"id":"2301.01716","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-01-04T17:29:04Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","stat.ML"],"title_canon_sha256":"950d4d9efb6b5c68a82cfdf4463be012a88b2b4666eae722df7268d4be912317","abstract_canon_sha256":"190702e046f429415e6dc7ed55682174eff4e97d2164fb5df3695fa1c64723b6"},"schema_version":"1.0"},"canonical_sha256":"e8c5dad03879003795e7bfb89a100d767f028bee83d64d5d2390ebd35cc5e07c","source":{"kind":"arxiv","id":"2301.01716","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.01716","created_at":"2026-07-05T07:53:06Z"},{"alias_kind":"arxiv_version","alias_value":"2301.01716v2","created_at":"2026-07-05T07:53:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.01716","created_at":"2026-07-05T07:53:06Z"},{"alias_kind":"pith_short_12","alias_value":"5DC5VUBYPEAD","created_at":"2026-07-05T07:53:06Z"},{"alias_kind":"pith_short_16","alias_value":"5DC5VUBYPEADPFPH","created_at":"2026-07-05T07:53:06Z"},{"alias_kind":"pith_short_8","alias_value":"5DC5VUBY","created_at":"2026-07-05T07:53:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:5DC5VUBYPEADPFPHX64JUEANOZ","target":"record","payload":{"canonical_record":{"source":{"id":"2301.01716","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-01-04T17:29:04Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","stat.ML"],"title_canon_sha256":"950d4d9efb6b5c68a82cfdf4463be012a88b2b4666eae722df7268d4be912317","abstract_canon_sha256":"190702e046f429415e6dc7ed55682174eff4e97d2164fb5df3695fa1c64723b6"},"schema_version":"1.0"},"canonical_sha256":"e8c5dad03879003795e7bfb89a100d767f028bee83d64d5d2390ebd35cc5e07c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:53:06.569277Z","signature_b64":"3gL2qaO+4dxRhclEhZr9cTtNU3EDmbBcxghz0MgYc4eVs6drgYXI1X6poO7FFaP53qx4cecZ0SOMylY39pEqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8c5dad03879003795e7bfb89a100d767f028bee83d64d5d2390ebd35cc5e07c","last_reissued_at":"2026-07-05T07:53:06.568798Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:53:06.568798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2301.01716","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:53:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cZY+4zHJmfGQO3guHuDfMZu1ruDiOGMSaKWet5EZZj1JCXJvcGGsPGBpl67qnSd1r5V+N5zfzvW90ZZz0Ml7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T16:40:47.671320Z"},"content_sha256":"a54c22bf91b9bad398c96dda2643f9c330dea686bb3dd949423b70fd15da3c06","schema_version":"1.0","event_id":"sha256:a54c22bf91b9bad398c96dda2643f9c330dea686bb3dd949423b70fd15da3c06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:5DC5VUBYPEADPFPHX64JUEANOZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"First-order penalty methods for bilevel optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA","stat.ML"],"primary_cat":"math.OC","authors_text":"Sanyou Mei, Zhaosong Lu","submitted_at":"2023-01-04T17:29:04Z","abstract_excerpt":"In this paper we study a class of unconstrained and constrained bilevel optimization problems in which the lower level is a possibly nonsmooth convex optimization problem, while the upper level is a possibly nonconvex optimization problem. We introduce a notion of $\\varepsilon$-KKT solution for them and show that an $\\varepsilon$-KKT solution leads to an $O(\\sqrt{\\varepsilon})$- or $O(\\varepsilon)$-hypergradient based stionary point under suitable assumptions. We also propose first-order penalty methods for finding an $\\varepsilon$-KKT solution of them, whose subproblems turn out to be a struc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.01716","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/2301.01716/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":"2026-07-05T07:53:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xoaPICf8uu2zFVrcNnolprSTMR9Bf4iQPq/P46ylDqiVwh17URi1EI5mDvy4gtHcWLWnzSHEyupK2ly22RaUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T16:40:47.672177Z"},"content_sha256":"b27321e8b1f25c876d1be33539f7bfcefb17384142e953de4de2e105929a67c4","schema_version":"1.0","event_id":"sha256:b27321e8b1f25c876d1be33539f7bfcefb17384142e953de4de2e105929a67c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5DC5VUBYPEADPFPHX64JUEANOZ/bundle.json","state_url":"https://pith.science/pith/5DC5VUBYPEADPFPHX64JUEANOZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5DC5VUBYPEADPFPHX64JUEANOZ/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":"2026-08-07T16:40:47Z","links":{"resolver":"https://pith.science/pith/5DC5VUBYPEADPFPHX64JUEANOZ","bundle":"https://pith.science/pith/5DC5VUBYPEADPFPHX64JUEANOZ/bundle.json","state":"https://pith.science/pith/5DC5VUBYPEADPFPHX64JUEANOZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5DC5VUBYPEADPFPHX64JUEANOZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:5DC5VUBYPEADPFPHX64JUEANOZ","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":"190702e046f429415e6dc7ed55682174eff4e97d2164fb5df3695fa1c64723b6","cross_cats_sorted":["cs.LG","cs.NA","math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-01-04T17:29:04Z","title_canon_sha256":"950d4d9efb6b5c68a82cfdf4463be012a88b2b4666eae722df7268d4be912317"},"schema_version":"1.0","source":{"id":"2301.01716","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.01716","created_at":"2026-07-05T07:53:06Z"},{"alias_kind":"arxiv_version","alias_value":"2301.01716v2","created_at":"2026-07-05T07:53:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.01716","created_at":"2026-07-05T07:53:06Z"},{"alias_kind":"pith_short_12","alias_value":"5DC5VUBYPEAD","created_at":"2026-07-05T07:53:06Z"},{"alias_kind":"pith_short_16","alias_value":"5DC5VUBYPEADPFPH","created_at":"2026-07-05T07:53:06Z"},{"alias_kind":"pith_short_8","alias_value":"5DC5VUBY","created_at":"2026-07-05T07:53:06Z"}],"graph_snapshots":[{"event_id":"sha256:b27321e8b1f25c876d1be33539f7bfcefb17384142e953de4de2e105929a67c4","target":"graph","created_at":"2026-07-05T07:53:06Z","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/2301.01716/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study a class of unconstrained and constrained bilevel optimization problems in which the lower level is a possibly nonsmooth convex optimization problem, while the upper level is a possibly nonconvex optimization problem. We introduce a notion of $\\varepsilon$-KKT solution for them and show that an $\\varepsilon$-KKT solution leads to an $O(\\sqrt{\\varepsilon})$- or $O(\\varepsilon)$-hypergradient based stionary point under suitable assumptions. We also propose first-order penalty methods for finding an $\\varepsilon$-KKT solution of them, whose subproblems turn out to be a struc","authors_text":"Sanyou Mei, Zhaosong Lu","cross_cats":["cs.LG","cs.NA","math.NA","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-01-04T17:29:04Z","title":"First-order penalty methods for bilevel optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.01716","kind":"arxiv","version":2},"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:a54c22bf91b9bad398c96dda2643f9c330dea686bb3dd949423b70fd15da3c06","target":"record","created_at":"2026-07-05T07:53:06Z","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":"190702e046f429415e6dc7ed55682174eff4e97d2164fb5df3695fa1c64723b6","cross_cats_sorted":["cs.LG","cs.NA","math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-01-04T17:29:04Z","title_canon_sha256":"950d4d9efb6b5c68a82cfdf4463be012a88b2b4666eae722df7268d4be912317"},"schema_version":"1.0","source":{"id":"2301.01716","kind":"arxiv","version":2}},"canonical_sha256":"e8c5dad03879003795e7bfb89a100d767f028bee83d64d5d2390ebd35cc5e07c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8c5dad03879003795e7bfb89a100d767f028bee83d64d5d2390ebd35cc5e07c","first_computed_at":"2026-07-05T07:53:06.568798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:53:06.568798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3gL2qaO+4dxRhclEhZr9cTtNU3EDmbBcxghz0MgYc4eVs6drgYXI1X6poO7FFaP53qx4cecZ0SOMylY39pEqAA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:53:06.569277Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.01716","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a54c22bf91b9bad398c96dda2643f9c330dea686bb3dd949423b70fd15da3c06","sha256:b27321e8b1f25c876d1be33539f7bfcefb17384142e953de4de2e105929a67c4"],"state_sha256":"6fd04e07ea7d0f708e66d2a6dd8a728733e6ac9f0ce858accba101f36ee878d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"syCI90wo0d9rxllwwhSWbD5+z4YaHZhhI5aKTOaH5FC694ExlPL1QAeTqEw/ZCW/av+BssqR9nvwMM/uO8LBAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T16:40:47.679318Z","bundle_sha256":"9b4ef9b40f21a42145c1eb93213cf1712cbc4842bc7d5852d13d262fbb96e739"}}