{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:54R34EZ3A7IDHZZKSAIJYPZCJV","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":"f054521dd9267cbbd6c94e00493f65a93451c1a5a1f3609ef93950ef1df0fd75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-03-18T11:31:55Z","title_canon_sha256":"b28201c8baf8954c0c0a5e6d0eb1b04a4adb933151d757284ae319214ce4e840"},"schema_version":"1.0","source":{"id":"1303.4212","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4212","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4212v2","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4212","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"pith_short_12","alias_value":"54R34EZ3A7ID","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"54R34EZ3A7IDHZZK","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"54R34EZ3","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:c9cee709fae1f521d18a9027974f936b17237c1ad74a5cf1d459e639134aa74e","target":"graph","created_at":"2026-05-18T00:56:06Z","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":"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","authors_text":"Carola Schrage, Giovanni P. Crespi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-03-18T11:31:55Z","title":"Set-optimization meets variational inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4212","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":"sha256:4d4d7bbe75d3c566e067a4e4b80908aea1284eb764989c189b549f92fb126ef2","target":"record","created_at":"2026-05-18T00:56:06Z","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":"f054521dd9267cbbd6c94e00493f65a93451c1a5a1f3609ef93950ef1df0fd75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-03-18T11:31:55Z","title_canon_sha256":"b28201c8baf8954c0c0a5e6d0eb1b04a4adb933151d757284ae319214ce4e840"},"schema_version":"1.0","source":{"id":"1303.4212","kind":"arxiv","version":2}},"canonical_sha256":"ef23be133b07d033e72a90109c3f224d5e724f526eaa2faf3b0f31d32ed8b3e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef23be133b07d033e72a90109c3f224d5e724f526eaa2faf3b0f31d32ed8b3e0","first_computed_at":"2026-05-18T00:56:06.731438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:06.731438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"413rI/Q3kN0/jBYsbWfp62T6SBFfeD0k03h9O4Dn4ArAYwGQ6S2iyykjw+BfakmVmo5GXeU6OlUmBzpgG1IpDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:06.732026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4212","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d4d7bbe75d3c566e067a4e4b80908aea1284eb764989c189b549f92fb126ef2","sha256:c9cee709fae1f521d18a9027974f936b17237c1ad74a5cf1d459e639134aa74e"],"state_sha256":"16ba77d02db60ae30573f8b2beea6e5150cc44bc9fe6d303fa58b714edeaf9d2"}