{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:H3G7TBUEFQ5LNFVCO4CFNNIAP4","short_pith_number":"pith:H3G7TBUE","canonical_record":{"source":{"id":"1802.02246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-06T22:10:14Z","cross_cats_sorted":[],"title_canon_sha256":"901ea8e0d2ed828193e7eca98695352b8d4d7e69883ed583670ee1eaf442cd8e","abstract_canon_sha256":"fc20ecfbd631385c10aebb62b239d4f2516ce35766dea62aba77e0517b73c718"},"schema_version":"1.0"},"canonical_sha256":"3ecdf986842c3ab696a2770456b5007f3c4a8a25bb68c1faf6e01bfe4c1955ce","source":{"kind":"arxiv","id":"1802.02246","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02246","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02246v1","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02246","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"pith_short_12","alias_value":"H3G7TBUEFQ5L","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H3G7TBUEFQ5LNFVC","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H3G7TBUE","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:H3G7TBUEFQ5LNFVCO4CFNNIAP4","target":"record","payload":{"canonical_record":{"source":{"id":"1802.02246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-06T22:10:14Z","cross_cats_sorted":[],"title_canon_sha256":"901ea8e0d2ed828193e7eca98695352b8d4d7e69883ed583670ee1eaf442cd8e","abstract_canon_sha256":"fc20ecfbd631385c10aebb62b239d4f2516ce35766dea62aba77e0517b73c718"},"schema_version":"1.0"},"canonical_sha256":"3ecdf986842c3ab696a2770456b5007f3c4a8a25bb68c1faf6e01bfe4c1955ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:08.791685Z","signature_b64":"oc3McL6uc4NzDNdxlFg7bJC6sJtQGJ/noAuET/0XKRRoVq2JdI+/5uGjf1AVcmL9N1akX2IuSey9RrVWlIPEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ecdf986842c3ab696a2770456b5007f3c4a8a25bb68c1faf6e01bfe4c1955ce","last_reissued_at":"2026-05-18T00:24:08.791000Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:08.791000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.02246","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vZmCJRuNfBmvdcv5KHazQ6MhhgFKqWULRs6g5JLseBafX9v1J4nR/KZA7wP/RxHyIC2SlvJCAqXC03yqd+FeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:18:30.666029Z"},"content_sha256":"ce9f044003d6cf980dbd1a19cc26340f7e57860a6ed2bcd5a6200ce8aa8870e9","schema_version":"1.0","event_id":"sha256:ce9f044003d6cf980dbd1a19cc26340f7e57860a6ed2bcd5a6200ce8aa8870e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:H3G7TBUEFQ5LNFVCO4CFNNIAP4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation Methods for Bilevel Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Mengdi Wang, Saeed Ghadimi","submitted_at":"2018-02-06T22:10:14Z","abstract_excerpt":"In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we present an approximation algorithm for solving this class of problem and provide its finite-time convergence analysis under different convexity assumption on the outer objective function. We also present an accelerated variant of this method which improves the rate of convergence under convexity assumption. Furthermore, we generalize our results under stocha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02246","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dZ7TyHvMN7oW0T4HMy1Yj/0g871xrNSjMelWQjbZ+HQUcxphDkLhIjJVAtlthcWhR5k2aIx28nIs+BPGpvwdCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:18:30.666395Z"},"content_sha256":"492c005aad35dfaec0be7d0b43fdb0d2c9f7d8bf273e845ce796fabf20cce6cf","schema_version":"1.0","event_id":"sha256:492c005aad35dfaec0be7d0b43fdb0d2c9f7d8bf273e845ce796fabf20cce6cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H3G7TBUEFQ5LNFVCO4CFNNIAP4/bundle.json","state_url":"https://pith.science/pith/H3G7TBUEFQ5LNFVCO4CFNNIAP4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H3G7TBUEFQ5LNFVCO4CFNNIAP4/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":"2026-05-28T19:18:30Z","links":{"resolver":"https://pith.science/pith/H3G7TBUEFQ5LNFVCO4CFNNIAP4","bundle":"https://pith.science/pith/H3G7TBUEFQ5LNFVCO4CFNNIAP4/bundle.json","state":"https://pith.science/pith/H3G7TBUEFQ5LNFVCO4CFNNIAP4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H3G7TBUEFQ5LNFVCO4CFNNIAP4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:H3G7TBUEFQ5LNFVCO4CFNNIAP4","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":"fc20ecfbd631385c10aebb62b239d4f2516ce35766dea62aba77e0517b73c718","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-06T22:10:14Z","title_canon_sha256":"901ea8e0d2ed828193e7eca98695352b8d4d7e69883ed583670ee1eaf442cd8e"},"schema_version":"1.0","source":{"id":"1802.02246","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02246","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02246v1","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02246","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"pith_short_12","alias_value":"H3G7TBUEFQ5L","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H3G7TBUEFQ5LNFVC","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H3G7TBUE","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:492c005aad35dfaec0be7d0b43fdb0d2c9f7d8bf273e845ce796fabf20cce6cf","target":"graph","created_at":"2026-05-18T00:24:08Z","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"},"paper":{"abstract_excerpt":"In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we present an approximation algorithm for solving this class of problem and provide its finite-time convergence analysis under different convexity assumption on the outer objective function. We also present an accelerated variant of this method which improves the rate of convergence under convexity assumption. Furthermore, we generalize our results under stocha","authors_text":"Mengdi Wang, Saeed Ghadimi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-06T22:10:14Z","title":"Approximation Methods for Bilevel Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02246","kind":"arxiv","version":1},"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:ce9f044003d6cf980dbd1a19cc26340f7e57860a6ed2bcd5a6200ce8aa8870e9","target":"record","created_at":"2026-05-18T00:24:08Z","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":"fc20ecfbd631385c10aebb62b239d4f2516ce35766dea62aba77e0517b73c718","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-06T22:10:14Z","title_canon_sha256":"901ea8e0d2ed828193e7eca98695352b8d4d7e69883ed583670ee1eaf442cd8e"},"schema_version":"1.0","source":{"id":"1802.02246","kind":"arxiv","version":1}},"canonical_sha256":"3ecdf986842c3ab696a2770456b5007f3c4a8a25bb68c1faf6e01bfe4c1955ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ecdf986842c3ab696a2770456b5007f3c4a8a25bb68c1faf6e01bfe4c1955ce","first_computed_at":"2026-05-18T00:24:08.791000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:08.791000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oc3McL6uc4NzDNdxlFg7bJC6sJtQGJ/noAuET/0XKRRoVq2JdI+/5uGjf1AVcmL9N1akX2IuSey9RrVWlIPEDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:08.791685Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.02246","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce9f044003d6cf980dbd1a19cc26340f7e57860a6ed2bcd5a6200ce8aa8870e9","sha256:492c005aad35dfaec0be7d0b43fdb0d2c9f7d8bf273e845ce796fabf20cce6cf"],"state_sha256":"6d2316fd89fc96db7c8045cfd20ac8f43214e1b8df7aa0b0da487bcb279a9e2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zV5PbvDg4ezGHW3UEfbTISIj1oxRERTQmMU3dQ59+14tIJADGMi7iyCcCIuLAufnF8pkmTksLBbG8wR8d8SSAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T19:18:30.668647Z","bundle_sha256":"fac6acdd4b5b2a0cfe4f45d163543c151b7eb39c967a55e0d61d29868fb78624"}}