{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:54R34EZ3A7IDHZZKSAIJYPZCJV","short_pith_number":"pith:54R34EZ3","schema_version":"1.0","canonical_sha256":"ef23be133b07d033e72a90109c3f224d5e724f526eaa2faf3b0f31d32ed8b3e0","source":{"kind":"arxiv","id":"1303.4212","version":2},"attestation_state":"computed","paper":{"title":"Set-optimization meets variational inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Carola Schrage, Giovanni P. Crespi","submitted_at":"2013-03-18T11:31:55Z","abstract_excerpt":"We study necessary and sufficient conditions to attain solutions of set-optimization problems in therms of variational inequalities of Stampacchia and Minty type. The notion of a solution we deal with has been introduced Heyde and Loehne, for convex set-valued objective functions. To define the set-valued variational inequality, we introduce a set-valued directional derivative and we relate it to the Dini derivatives of a family of linearly scalarized problems. The optimality conditions are given by Stampacchia and Minty type Variational inequalities, defined both by the set valued directional"},"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":"1303.4212","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-03-18T11:31:55Z","cross_cats_sorted":[],"title_canon_sha256":"b28201c8baf8954c0c0a5e6d0eb1b04a4adb933151d757284ae319214ce4e840","abstract_canon_sha256":"f054521dd9267cbbd6c94e00493f65a93451c1a5a1f3609ef93950ef1df0fd75"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:06.732026Z","signature_b64":"413rI/Q3kN0/jBYsbWfp62T6SBFfeD0k03h9O4Dn4ArAYwGQ6S2iyykjw+BfakmVmo5GXeU6OlUmBzpgG1IpDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef23be133b07d033e72a90109c3f224d5e724f526eaa2faf3b0f31d32ed8b3e0","last_reissued_at":"2026-05-18T00:56:06.731438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:06.731438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Set-optimization meets variational inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Carola Schrage, Giovanni P. Crespi","submitted_at":"2013-03-18T11:31:55Z","abstract_excerpt":"We study necessary and sufficient conditions to attain solutions of set-optimization problems in therms of variational inequalities of Stampacchia and Minty type. The notion of a solution we deal with has been introduced Heyde and Loehne, for convex set-valued objective functions. To define the set-valued variational inequality, we introduce a set-valued directional derivative and we relate it to the Dini derivatives of a family of linearly scalarized problems. The optimality conditions are given by Stampacchia and Minty type Variational inequalities, defined both by the set valued directional"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4212","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.4212","created_at":"2026-05-18T00:56:06.731562+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.4212v2","created_at":"2026-05-18T00:56:06.731562+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4212","created_at":"2026-05-18T00:56:06.731562+00:00"},{"alias_kind":"pith_short_12","alias_value":"54R34EZ3A7ID","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"54R34EZ3A7IDHZZK","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"54R34EZ3","created_at":"2026-05-18T12:27:34.582898+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/54R34EZ3A7IDHZZKSAIJYPZCJV","json":"https://pith.science/pith/54R34EZ3A7IDHZZKSAIJYPZCJV.json","graph_json":"https://pith.science/api/pith-number/54R34EZ3A7IDHZZKSAIJYPZCJV/graph.json","events_json":"https://pith.science/api/pith-number/54R34EZ3A7IDHZZKSAIJYPZCJV/events.json","paper":"https://pith.science/paper/54R34EZ3"},"agent_actions":{"view_html":"https://pith.science/pith/54R34EZ3A7IDHZZKSAIJYPZCJV","download_json":"https://pith.science/pith/54R34EZ3A7IDHZZKSAIJYPZCJV.json","view_paper":"https://pith.science/paper/54R34EZ3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.4212&json=true","fetch_graph":"https://pith.science/api/pith-number/54R34EZ3A7IDHZZKSAIJYPZCJV/graph.json","fetch_events":"https://pith.science/api/pith-number/54R34EZ3A7IDHZZKSAIJYPZCJV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/54R34EZ3A7IDHZZKSAIJYPZCJV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/54R34EZ3A7IDHZZKSAIJYPZCJV/action/storage_attestation","attest_author":"https://pith.science/pith/54R34EZ3A7IDHZZKSAIJYPZCJV/action/author_attestation","sign_citation":"https://pith.science/pith/54R34EZ3A7IDHZZKSAIJYPZCJV/action/citation_signature","submit_replication":"https://pith.science/pith/54R34EZ3A7IDHZZKSAIJYPZCJV/action/replication_record"}},"created_at":"2026-05-18T00:56:06.731562+00:00","updated_at":"2026-05-18T00:56:06.731562+00:00"}