{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:O5HM6L5WDESDCTCVZ3HBWRRBMS","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":"ffd2667ec31fb3f7e2887b9d54bb7f0537e60b60830c49da2e0c4be50c411bfc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-16T07:03:02Z","title_canon_sha256":"fe39de6529e99bd96a539883eb507650c70ae152fa1867b31bfe65296de5bef6"},"schema_version":"1.0","source":{"id":"1906.06656","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.06656","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"arxiv_version","alias_value":"1906.06656v1","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.06656","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"pith_short_12","alias_value":"O5HM6L5WDESD","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"O5HM6L5WDESDCTCV","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"O5HM6L5W","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:9bdb3a991cf837b1942c29d2cbf6d875f13bdd1e85bfa3890607ee0be03501fe","target":"graph","created_at":"2026-05-17T23:43:13Z","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":"In this paper, we study the norm-based robust (efficient) solutions of a Vector Optimization Problem (VOP). We define two kinds of non-ascent directions in terms of Clarke's generalized gradient and characterize norm-based robustness by means of the newly-defined directions. This is done under a basic Constraint Qualification (CQ). We extend the provided characterization to VOPs with conic constraints. Moreover, we derive a necessary condition for norm-based robustness utilizing a nonsmooth gap function.","authors_text":"Majid Soleimani-damaneh, Morteza Rahimi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-16T07:03:02Z","title":"Characterization of the norm-based robust solutions in vector optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.06656","kind":"arxiv","version":1},"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":"sha256:10cc1c63797044e74d42634521f9ef2b5ebf814dfb3fa508f24ef7946523f130","target":"record","created_at":"2026-05-17T23:43:13Z","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":"ffd2667ec31fb3f7e2887b9d54bb7f0537e60b60830c49da2e0c4be50c411bfc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-16T07:03:02Z","title_canon_sha256":"fe39de6529e99bd96a539883eb507650c70ae152fa1867b31bfe65296de5bef6"},"schema_version":"1.0","source":{"id":"1906.06656","kind":"arxiv","version":1}},"canonical_sha256":"774ecf2fb61924314c55cece1b462164a14df732264893144fa350a74acbc226","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"774ecf2fb61924314c55cece1b462164a14df732264893144fa350a74acbc226","first_computed_at":"2026-05-17T23:43:13.019460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:13.019460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TRbWXNlR2yY0/MYp4iWEC7EUYQeBdjy7BSOOYbrL0Wgm5E3wr52DeJgF3F6OfgBrPK/CkMRhr8cNOLfWogwSAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:13.019942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.06656","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10cc1c63797044e74d42634521f9ef2b5ebf814dfb3fa508f24ef7946523f130","sha256:9bdb3a991cf837b1942c29d2cbf6d875f13bdd1e85bfa3890607ee0be03501fe"],"state_sha256":"d5dfa636499da2f9cd094cadf949d0062aa28932c42f6ca2c6fa4a7620f37587"}