{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:MQPGIFIDTUAITMHNN25B5NBNSR","short_pith_number":"pith:MQPGIFID","schema_version":"1.0","canonical_sha256":"641e6415039d0089b0ed6eba1eb42d945fe3f54daf67e3e7f22184e143106583","source":{"kind":"arxiv","id":"1612.00255","version":1},"attestation_state":"computed","paper":{"title":"Remarks on Lagrange Multiplier Rules in Set Valued Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Carola Schrage","submitted_at":"2016-12-01T14:08:35Z","abstract_excerpt":"In this note, three Lagrange multiplier rules introduced in the literature for set valued optimization problems are compared. A generalization of all three results is given which proves that under rather mild assumptions, $x$ is a weak solution to the constrained problem, if and only if it is a weak solution to the Lagrangian."},"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":"1612.00255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-01T14:08:35Z","cross_cats_sorted":[],"title_canon_sha256":"910fc1b79804c22bf8f597c0095f919a16cdc41da0b0ad6fa8a9ea31ade3990e","abstract_canon_sha256":"6f3b465d495b28aa6437b794a1a313db866d9a05630059f177a6b524f9322e67"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:05.616736Z","signature_b64":"YqYPWqnGjxv47uHC+JKDY8N9HP/ZZcg2CRKRwDefprOnF5UOhgFTQMP6LUTjTLYTWX78zpdBdwzMFo9zWRLLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"641e6415039d0089b0ed6eba1eb42d945fe3f54daf67e3e7f22184e143106583","last_reissued_at":"2026-05-18T00:56:05.616139Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:05.616139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remarks on Lagrange Multiplier Rules in Set Valued Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Carola Schrage","submitted_at":"2016-12-01T14:08:35Z","abstract_excerpt":"In this note, three Lagrange multiplier rules introduced in the literature for set valued optimization problems are compared. A generalization of all three results is given which proves that under rather mild assumptions, $x$ is a weak solution to the constrained problem, if and only if it is a weak solution to the Lagrangian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00255","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":"1612.00255","created_at":"2026-05-18T00:56:05.616222+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.00255v1","created_at":"2026-05-18T00:56:05.616222+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00255","created_at":"2026-05-18T00:56:05.616222+00:00"},{"alias_kind":"pith_short_12","alias_value":"MQPGIFIDTUAI","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MQPGIFIDTUAITMHN","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MQPGIFID","created_at":"2026-05-18T12:30:32.724797+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/MQPGIFIDTUAITMHNN25B5NBNSR","json":"https://pith.science/pith/MQPGIFIDTUAITMHNN25B5NBNSR.json","graph_json":"https://pith.science/api/pith-number/MQPGIFIDTUAITMHNN25B5NBNSR/graph.json","events_json":"https://pith.science/api/pith-number/MQPGIFIDTUAITMHNN25B5NBNSR/events.json","paper":"https://pith.science/paper/MQPGIFID"},"agent_actions":{"view_html":"https://pith.science/pith/MQPGIFIDTUAITMHNN25B5NBNSR","download_json":"https://pith.science/pith/MQPGIFIDTUAITMHNN25B5NBNSR.json","view_paper":"https://pith.science/paper/MQPGIFID","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.00255&json=true","fetch_graph":"https://pith.science/api/pith-number/MQPGIFIDTUAITMHNN25B5NBNSR/graph.json","fetch_events":"https://pith.science/api/pith-number/MQPGIFIDTUAITMHNN25B5NBNSR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MQPGIFIDTUAITMHNN25B5NBNSR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MQPGIFIDTUAITMHNN25B5NBNSR/action/storage_attestation","attest_author":"https://pith.science/pith/MQPGIFIDTUAITMHNN25B5NBNSR/action/author_attestation","sign_citation":"https://pith.science/pith/MQPGIFIDTUAITMHNN25B5NBNSR/action/citation_signature","submit_replication":"https://pith.science/pith/MQPGIFIDTUAITMHNN25B5NBNSR/action/replication_record"}},"created_at":"2026-05-18T00:56:05.616222+00:00","updated_at":"2026-05-18T00:56:05.616222+00:00"}