{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:BHHQTB5Q3HR7E7LPKDPS2ACDFO","short_pith_number":"pith:BHHQTB5Q","schema_version":"1.0","canonical_sha256":"09cf0987b0d9e3f27d6f50df2d00432ba2eeac4068bd73fa622203487323a11c","source":{"kind":"arxiv","id":"1807.07554","version":1},"attestation_state":"computed","paper":{"title":"A geometric integration approach to nonsmooth, nonconvex optimisation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Carola-Bibiane Sch\\\"onlieb, Erlend S. Riis, G. R. W. Quispel, Matthias J. Ehrhardt","submitted_at":"2018-07-19T17:52:59Z","abstract_excerpt":"The optimisation of nonsmooth, nonconvex functions without access to gradients is a particularly challenging problem that is frequently encountered, for example in model parameter optimisation problems. Bilevel optimisation of parameters is a standard setting in areas such as variational regularisation problems and supervised machine learning. We present efficient and robust derivative-free methods called randomised Itoh--Abe methods. These are generalisations of the Itoh--Abe discrete gradient method, a well-known scheme from geometric integration, which has previously only been considered in"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1807.07554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-19T17:52:59Z","cross_cats_sorted":[],"title_canon_sha256":"a78511542d35c011fb2ef10805213ba93b597134b9f33bc74a30f808dbc8156b","abstract_canon_sha256":"e39322ea70df15be06237186cd855968fd9b1e91c8ee0f4b2ab569cbafc422b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:19.909058Z","signature_b64":"vFKG8w8gqAPn49fKCp1dc3x1vm7RwJ5esO8CmKarPKNeMspjDPRFNJnYvMC4MpqnVl3CPD86vGSSj+iMJMruBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09cf0987b0d9e3f27d6f50df2d00432ba2eeac4068bd73fa622203487323a11c","last_reissued_at":"2026-05-18T00:10:19.908246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:19.908246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A geometric integration approach to nonsmooth, nonconvex optimisation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Carola-Bibiane Sch\\\"onlieb, Erlend S. Riis, G. R. W. Quispel, Matthias J. Ehrhardt","submitted_at":"2018-07-19T17:52:59Z","abstract_excerpt":"The optimisation of nonsmooth, nonconvex functions without access to gradients is a particularly challenging problem that is frequently encountered, for example in model parameter optimisation problems. Bilevel optimisation of parameters is a standard setting in areas such as variational regularisation problems and supervised machine learning. We present efficient and robust derivative-free methods called randomised Itoh--Abe methods. These are generalisations of the Itoh--Abe discrete gradient method, a well-known scheme from geometric integration, which has previously only been considered in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07554","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.07554","created_at":"2026-05-18T00:10:19.908381+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.07554v1","created_at":"2026-05-18T00:10:19.908381+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07554","created_at":"2026-05-18T00:10:19.908381+00:00"},{"alias_kind":"pith_short_12","alias_value":"BHHQTB5Q3HR7","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"BHHQTB5Q3HR7E7LP","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"BHHQTB5Q","created_at":"2026-05-18T12:32:16.446611+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BHHQTB5Q3HR7E7LPKDPS2ACDFO","json":"https://pith.science/pith/BHHQTB5Q3HR7E7LPKDPS2ACDFO.json","graph_json":"https://pith.science/api/pith-number/BHHQTB5Q3HR7E7LPKDPS2ACDFO/graph.json","events_json":"https://pith.science/api/pith-number/BHHQTB5Q3HR7E7LPKDPS2ACDFO/events.json","paper":"https://pith.science/paper/BHHQTB5Q"},"agent_actions":{"view_html":"https://pith.science/pith/BHHQTB5Q3HR7E7LPKDPS2ACDFO","download_json":"https://pith.science/pith/BHHQTB5Q3HR7E7LPKDPS2ACDFO.json","view_paper":"https://pith.science/paper/BHHQTB5Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.07554&json=true","fetch_graph":"https://pith.science/api/pith-number/BHHQTB5Q3HR7E7LPKDPS2ACDFO/graph.json","fetch_events":"https://pith.science/api/pith-number/BHHQTB5Q3HR7E7LPKDPS2ACDFO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BHHQTB5Q3HR7E7LPKDPS2ACDFO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BHHQTB5Q3HR7E7LPKDPS2ACDFO/action/storage_attestation","attest_author":"https://pith.science/pith/BHHQTB5Q3HR7E7LPKDPS2ACDFO/action/author_attestation","sign_citation":"https://pith.science/pith/BHHQTB5Q3HR7E7LPKDPS2ACDFO/action/citation_signature","submit_replication":"https://pith.science/pith/BHHQTB5Q3HR7E7LPKDPS2ACDFO/action/replication_record"}},"created_at":"2026-05-18T00:10:19.908381+00:00","updated_at":"2026-05-18T00:10:19.908381+00:00"}