{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RUFWL4Z2KJT6T33KPRVTV7JUCQ","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":"d607f418dbdec4f15c7894419500de0412d858e9798fa5f2fae35c6766d71267","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-17T11:27:48Z","title_canon_sha256":"8f0ba548d624b941ff30af24abda31f45e4dd37c65516736656c28d85f8a6752"},"schema_version":"1.0","source":{"id":"1105.3343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3343","created_at":"2026-05-18T04:22:00Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3343v1","created_at":"2026-05-18T04:22:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3343","created_at":"2026-05-18T04:22:00Z"},{"alias_kind":"pith_short_12","alias_value":"RUFWL4Z2KJT6","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RUFWL4Z2KJT6T33K","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RUFWL4Z2","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:5cd75694004a3b0e2e82aee07512e3ed5133fa463c1d4b2754d739f3939d6af5","target":"graph","created_at":"2026-05-18T04:22:00Z","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":"A mathematical programming problem with affine equilibrium constraints (AMPEC) is a bilevel programming problem where the lower one is a parametric affine variational inequality. We formulate some classes of bilevel programming in forms of MPEC. Then we use a regularization technique to formulate the resulting problem as a mathematical program with an additional constraint defined by the difference of two convex functions (DC function). A main feature of this DC decomposition is that the second component depends upon only the parameter in the lower problem. This property allows us to develop b","authors_text":"Le Dung Muu, Le Thi Hoai An, Pham Dinh Tao, Tran Dinh Quoc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-17T11:27:48Z","title":"Decomposition algorithms for globally solving mathematical programs with affine equilibrium constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3343","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":"sha256:5bd37cdcd0b2671a9f67db367574939e9dc106f081a60d6408f96a0b1ac07710","target":"record","created_at":"2026-05-18T04:22:00Z","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":"d607f418dbdec4f15c7894419500de0412d858e9798fa5f2fae35c6766d71267","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-05-17T11:27:48Z","title_canon_sha256":"8f0ba548d624b941ff30af24abda31f45e4dd37c65516736656c28d85f8a6752"},"schema_version":"1.0","source":{"id":"1105.3343","kind":"arxiv","version":1}},"canonical_sha256":"8d0b65f33a5267e9ef6a7c6b3afd341421499c6daff3ece161b68a0f5448dc33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d0b65f33a5267e9ef6a7c6b3afd341421499c6daff3ece161b68a0f5448dc33","first_computed_at":"2026-05-18T04:22:00.218350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:00.218350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HK3qEcQQ9keJQrXxN7oU7uoFQ8Iby/VVy2O7uGF0+uetK8Pr2YyQsUgYtAkZeroehD0ncSrjxq7ig7bqo6yYBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:00.218850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bd37cdcd0b2671a9f67db367574939e9dc106f081a60d6408f96a0b1ac07710","sha256:5cd75694004a3b0e2e82aee07512e3ed5133fa463c1d4b2754d739f3939d6af5"],"state_sha256":"1f62a46afa27ec7651f5e3abb84d152bb0df5ea4474c3a5f5eece315dda3b83b"}