{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:JFD6OB5W5HAX6FIGOYXQI744MI","short_pith_number":"pith:JFD6OB5W","canonical_record":{"source":{"id":"1806.05896","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-15T10:36:09Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"047bcdc7a3a2d3b5190f742e91c69e8ad95927b935eca4f24269f96b078dcb31","abstract_canon_sha256":"1abf51fed2770fc76abfd12c6678018ba93f689d99e495aaf951bef6b8317d9c"},"schema_version":"1.0"},"canonical_sha256":"4947e707b6e9c17f1506762f047f9c623963b8a52dcc22fbad72253dfcab2449","source":{"kind":"arxiv","id":"1806.05896","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05896","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05896v2","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05896","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"pith_short_12","alias_value":"JFD6OB5W5HAX","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JFD6OB5W5HAX6FIG","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JFD6OB5W","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:JFD6OB5W5HAX6FIGOYXQI744MI","target":"record","payload":{"canonical_record":{"source":{"id":"1806.05896","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-15T10:36:09Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"047bcdc7a3a2d3b5190f742e91c69e8ad95927b935eca4f24269f96b078dcb31","abstract_canon_sha256":"1abf51fed2770fc76abfd12c6678018ba93f689d99e495aaf951bef6b8317d9c"},"schema_version":"1.0"},"canonical_sha256":"4947e707b6e9c17f1506762f047f9c623963b8a52dcc22fbad72253dfcab2449","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:16.408669Z","signature_b64":"mKAy6w2V49SQLCKf/JxYgG3S273BKfjhm/mgHfEfNtitSzYAMmVSA2GJHtgoJaCbZrukwtDYrZRpSngKr/pfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4947e707b6e9c17f1506762f047f9c623963b8a52dcc22fbad72253dfcab2449","last_reissued_at":"2026-05-17T23:54:16.408225Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:16.408225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.05896","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":"2026-05-17T23:54:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lA9v43S0lM9h5c691JIH+QXi40F0t83QSwTPXeLSNuwMhKs7NVSuHS6tIsyJ0IgT6Pi9hM4EK740BLwIBYd9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T21:48:19.008934Z"},"content_sha256":"1d4a9bc8bc472a354c45118fe1c7099f1bd7c2b545c1aa366ba840e68b89bff1","schema_version":"1.0","event_id":"sha256:1d4a9bc8bc472a354c45118fe1c7099f1bd7c2b545c1aa366ba840e68b89bff1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:JFD6OB5W5HAX6FIGOYXQI744MI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interior Point Methods and Preconditioning for PDE-Constrained Optimization Problems Involving Sparsity Terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.OC","authors_text":"John W. Pearson, Margherita Porcelli, Martin Stoll","submitted_at":"2018-06-15T10:36:09Z","abstract_excerpt":"PDE-constrained optimization problems with control or state constraints are challenging from an analytical as well as numerical perspective. The combination of these constraints with a sparsity-promoting $\\rm L^1$ term within the objective function requires sophisticated optimization methods. We propose the use of an Interior Point scheme applied to a smoothed reformulation of the discretized problem, and illustrate that such a scheme exhibits robust performance with respect to parameter changes. To increase the potency of this method we introduce fast and efficient preconditioners which enabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05896","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":""},"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":"2026-05-17T23:54:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w1Utk3VPV+xr5QlCFsOnfXgAfEPy6SONqew6akU9vIk08jKeZZyFYPAY6LN8tOQPbJebhTMuFYeR4N3oT2c4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T21:48:19.009278Z"},"content_sha256":"7e7c6dab61632254eed41d69e0b7f19da88e62262a7eeb3ba0d01fab487a70a2","schema_version":"1.0","event_id":"sha256:7e7c6dab61632254eed41d69e0b7f19da88e62262a7eeb3ba0d01fab487a70a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JFD6OB5W5HAX6FIGOYXQI744MI/bundle.json","state_url":"https://pith.science/pith/JFD6OB5W5HAX6FIGOYXQI744MI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JFD6OB5W5HAX6FIGOYXQI744MI/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":"2026-07-02T21:48:19Z","links":{"resolver":"https://pith.science/pith/JFD6OB5W5HAX6FIGOYXQI744MI","bundle":"https://pith.science/pith/JFD6OB5W5HAX6FIGOYXQI744MI/bundle.json","state":"https://pith.science/pith/JFD6OB5W5HAX6FIGOYXQI744MI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JFD6OB5W5HAX6FIGOYXQI744MI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JFD6OB5W5HAX6FIGOYXQI744MI","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":"1abf51fed2770fc76abfd12c6678018ba93f689d99e495aaf951bef6b8317d9c","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-15T10:36:09Z","title_canon_sha256":"047bcdc7a3a2d3b5190f742e91c69e8ad95927b935eca4f24269f96b078dcb31"},"schema_version":"1.0","source":{"id":"1806.05896","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05896","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05896v2","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05896","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"pith_short_12","alias_value":"JFD6OB5W5HAX","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JFD6OB5W5HAX6FIG","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JFD6OB5W","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:7e7c6dab61632254eed41d69e0b7f19da88e62262a7eeb3ba0d01fab487a70a2","target":"graph","created_at":"2026-05-17T23:54:16Z","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":"PDE-constrained optimization problems with control or state constraints are challenging from an analytical as well as numerical perspective. The combination of these constraints with a sparsity-promoting $\\rm L^1$ term within the objective function requires sophisticated optimization methods. We propose the use of an Interior Point scheme applied to a smoothed reformulation of the discretized problem, and illustrate that such a scheme exhibits robust performance with respect to parameter changes. To increase the potency of this method we introduce fast and efficient preconditioners which enabl","authors_text":"John W. Pearson, Margherita Porcelli, Martin Stoll","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-15T10:36:09Z","title":"Interior Point Methods and Preconditioning for PDE-Constrained Optimization Problems Involving Sparsity Terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05896","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":"sha256:1d4a9bc8bc472a354c45118fe1c7099f1bd7c2b545c1aa366ba840e68b89bff1","target":"record","created_at":"2026-05-17T23:54:16Z","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":"1abf51fed2770fc76abfd12c6678018ba93f689d99e495aaf951bef6b8317d9c","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-15T10:36:09Z","title_canon_sha256":"047bcdc7a3a2d3b5190f742e91c69e8ad95927b935eca4f24269f96b078dcb31"},"schema_version":"1.0","source":{"id":"1806.05896","kind":"arxiv","version":2}},"canonical_sha256":"4947e707b6e9c17f1506762f047f9c623963b8a52dcc22fbad72253dfcab2449","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4947e707b6e9c17f1506762f047f9c623963b8a52dcc22fbad72253dfcab2449","first_computed_at":"2026-05-17T23:54:16.408225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:16.408225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mKAy6w2V49SQLCKf/JxYgG3S273BKfjhm/mgHfEfNtitSzYAMmVSA2GJHtgoJaCbZrukwtDYrZRpSngKr/pfAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:16.408669Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05896","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d4a9bc8bc472a354c45118fe1c7099f1bd7c2b545c1aa366ba840e68b89bff1","sha256:7e7c6dab61632254eed41d69e0b7f19da88e62262a7eeb3ba0d01fab487a70a2"],"state_sha256":"58224f866c6ebcf5361b082a5e1ed84d0d3e3b150cad3f2a964161dd6f9118d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P8qznj14OYRtSiiiOU2JVlEFQaaC0A/0EXOEj5Bc2AUH8BJxUI0G6PrSwhhnNtFwjzYu0X4KoVNcCEfZ1yEaAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T21:48:19.011211Z","bundle_sha256":"93102f0b8a42c90c71ad579a086c5abd796ff7a3c191c4b7266d078e41392b70"}}