{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:36QBZSLZLNXAM37A37ABEVO76V","short_pith_number":"pith:36QBZSLZ","canonical_record":{"source":{"id":"1810.01923","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-03T19:25:18Z","cross_cats_sorted":[],"title_canon_sha256":"8f11a52110e2d7a55f6711b2efc487741c375e1d530852761d1d7b8669d47ec8","abstract_canon_sha256":"3a722332a75ef4d1afc5aea0a35fecce45089c9935139d4dbca0575641fc6dac"},"schema_version":"1.0"},"canonical_sha256":"dfa01cc9795b6e066fe0dfc01255dff569cc67977ab9d3f48a220e4171e45482","source":{"kind":"arxiv","id":"1810.01923","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.01923","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"1810.01923v1","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01923","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"36QBZSLZLNXA","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"36QBZSLZLNXAM37A","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"36QBZSLZ","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:36QBZSLZLNXAM37A37ABEVO76V","target":"record","payload":{"canonical_record":{"source":{"id":"1810.01923","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-03T19:25:18Z","cross_cats_sorted":[],"title_canon_sha256":"8f11a52110e2d7a55f6711b2efc487741c375e1d530852761d1d7b8669d47ec8","abstract_canon_sha256":"3a722332a75ef4d1afc5aea0a35fecce45089c9935139d4dbca0575641fc6dac"},"schema_version":"1.0"},"canonical_sha256":"dfa01cc9795b6e066fe0dfc01255dff569cc67977ab9d3f48a220e4171e45482","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:06.950624Z","signature_b64":"YLZ/vq1mqXS4loQEkWNnSe5SnWhgp04tlu2p/5Yw0+RgWvsT/75y7LjbH4G/8fPaRjnXPIE/lphEHaQQGP2nBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfa01cc9795b6e066fe0dfc01255dff569cc67977ab9d3f48a220e4171e45482","last_reissued_at":"2026-05-18T00:04:06.949993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:06.949993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.01923","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":"2026-05-18T00:04:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FwPJwi5FfF4kMBZwqukR0deALvrQpkCCf9ER8oyTkzQKi60ZgEQdyU1iZxkVuTiq/mf/82TTtPz0o1SYPpCOCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T11:51:59.235768Z"},"content_sha256":"719a8366327a3186e7c7d503e06a99507b7286e3e1fa3e23bb716522a7bf78bd","schema_version":"1.0","event_id":"sha256:719a8366327a3186e7c7d503e06a99507b7286e3e1fa3e23bb716522a7bf78bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:36QBZSLZLNXAM37A37ABEVO76V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An FE-dABCD algorithm for elliptic optimal control problems with constraints on the gradient of the state and control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bo Yu, Xiaoliang Song, Xiaotong Chen, Zixuan Chen","submitted_at":"2018-10-03T19:25:18Z","abstract_excerpt":"In this paper, elliptic control problems with integral constraint on the gradient of the state and box constraints on the control are considered. The optimal conditions of the problem are proved. To numerically solve the problem, we use the 'First discretize, then optimize' approach. Specifically, we discretize both the state and the control by piecewise linear functions. To solve the discretized problem efficiently, we first transform it into a multi-block unconstrained convex optimization problem via its dual, then we extend the inexact majorized accelerating block coordinate descent (imABCD"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01923","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":"2026-05-18T00:04:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"88pdIHYtIeBw2Qh6R34/lbsUeh1ShngYXkiuVaBnBRGet5Y+FVbTtcRVx9R1aWlvjuj6YEBoy70dupiIjuybCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T11:51:59.236154Z"},"content_sha256":"d9fc3bc0cb77b744d1450124dffd275c5e61f446890e050db8923701e897113b","schema_version":"1.0","event_id":"sha256:d9fc3bc0cb77b744d1450124dffd275c5e61f446890e050db8923701e897113b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/36QBZSLZLNXAM37A37ABEVO76V/bundle.json","state_url":"https://pith.science/pith/36QBZSLZLNXAM37A37ABEVO76V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/36QBZSLZLNXAM37A37ABEVO76V/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":"2026-05-19T11:51:59Z","links":{"resolver":"https://pith.science/pith/36QBZSLZLNXAM37A37ABEVO76V","bundle":"https://pith.science/pith/36QBZSLZLNXAM37A37ABEVO76V/bundle.json","state":"https://pith.science/pith/36QBZSLZLNXAM37A37ABEVO76V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/36QBZSLZLNXAM37A37ABEVO76V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:36QBZSLZLNXAM37A37ABEVO76V","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":"3a722332a75ef4d1afc5aea0a35fecce45089c9935139d4dbca0575641fc6dac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-03T19:25:18Z","title_canon_sha256":"8f11a52110e2d7a55f6711b2efc487741c375e1d530852761d1d7b8669d47ec8"},"schema_version":"1.0","source":{"id":"1810.01923","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.01923","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"1810.01923v1","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01923","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"36QBZSLZLNXA","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"36QBZSLZLNXAM37A","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"36QBZSLZ","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:d9fc3bc0cb77b744d1450124dffd275c5e61f446890e050db8923701e897113b","target":"graph","created_at":"2026-05-18T00:04:06Z","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"},"paper":{"abstract_excerpt":"In this paper, elliptic control problems with integral constraint on the gradient of the state and box constraints on the control are considered. The optimal conditions of the problem are proved. To numerically solve the problem, we use the 'First discretize, then optimize' approach. Specifically, we discretize both the state and the control by piecewise linear functions. To solve the discretized problem efficiently, we first transform it into a multi-block unconstrained convex optimization problem via its dual, then we extend the inexact majorized accelerating block coordinate descent (imABCD","authors_text":"Bo Yu, Xiaoliang Song, Xiaotong Chen, Zixuan Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-03T19:25:18Z","title":"An FE-dABCD algorithm for elliptic optimal control problems with constraints on the gradient of the state and control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01923","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":"sha256:719a8366327a3186e7c7d503e06a99507b7286e3e1fa3e23bb716522a7bf78bd","target":"record","created_at":"2026-05-18T00:04:06Z","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":"3a722332a75ef4d1afc5aea0a35fecce45089c9935139d4dbca0575641fc6dac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-10-03T19:25:18Z","title_canon_sha256":"8f11a52110e2d7a55f6711b2efc487741c375e1d530852761d1d7b8669d47ec8"},"schema_version":"1.0","source":{"id":"1810.01923","kind":"arxiv","version":1}},"canonical_sha256":"dfa01cc9795b6e066fe0dfc01255dff569cc67977ab9d3f48a220e4171e45482","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfa01cc9795b6e066fe0dfc01255dff569cc67977ab9d3f48a220e4171e45482","first_computed_at":"2026-05-18T00:04:06.949993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:06.949993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YLZ/vq1mqXS4loQEkWNnSe5SnWhgp04tlu2p/5Yw0+RgWvsT/75y7LjbH4G/8fPaRjnXPIE/lphEHaQQGP2nBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:06.950624Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.01923","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:719a8366327a3186e7c7d503e06a99507b7286e3e1fa3e23bb716522a7bf78bd","sha256:d9fc3bc0cb77b744d1450124dffd275c5e61f446890e050db8923701e897113b"],"state_sha256":"94fa510b1f67a75e7c3c5b60cb3f06cadc975ee928045d1cd7c1ac3ddb64cc4d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n7ONoXtsP5cUwoowHCQkjH5k4n2DFxQVLd8FF+xSJSS2pl/eGaQNL57QhI1n6rxFomvdu5DOKbAT0iqkO0BLBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T11:51:59.237790Z","bundle_sha256":"c99ae617d08c1e111d20af259a84f19811d7a4e2553ddb73eef8de1f47639e38"}}