{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Z57CZOHSBT2GI6ZPEEMLH3AEOZ","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":"4e0fa18b1c099136c4d574421152b59a769b08c0c3e74977e87a96ff7b29f70c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-07T17:15:26Z","title_canon_sha256":"2ad41717a4125c0229550237961bc89e1e511704838fb7ac6b31d4e26f3e24a7"},"schema_version":"1.0","source":{"id":"1801.02218","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.02218","created_at":"2026-05-18T00:26:34Z"},{"alias_kind":"arxiv_version","alias_value":"1801.02218v1","created_at":"2026-05-18T00:26:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02218","created_at":"2026-05-18T00:26:34Z"},{"alias_kind":"pith_short_12","alias_value":"Z57CZOHSBT2G","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Z57CZOHSBT2GI6ZP","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Z57CZOHS","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:a871bc88c8742c77c2659aabb24b9dfa6f89f7b4b7577e951f14478805d67772","target":"graph","created_at":"2026-05-18T00:26:34Z","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":"It was proved in [14] that the existence of a noncritical multiplier for a (smooth) nonlinear programming problem is equivalent to an error bound condition for the Karush-Kuhn-Thcker (KKT) system without any assumptions. This paper investigates whether this result still holds true for a (smooth) nonlinear semidefinite programming (SDP) problem. We first introduce the notion of critical and noncritical multipliers for a SDP problem and obtain their complete characterizations in terms of the problem data. We prove for the SDP problem, the noncriticality property can be derived from the error bou","authors_text":"Liwei Zhang, Tianyu Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-07T17:15:26Z","title":"Critical Multipliers in Semidefinite Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02218","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":"sha256:46c41e7b4182bda7f8b88b67786bf9797d889a5110c9adbf1c08c43332979442","target":"record","created_at":"2026-05-18T00:26:34Z","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":"4e0fa18b1c099136c4d574421152b59a769b08c0c3e74977e87a96ff7b29f70c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-07T17:15:26Z","title_canon_sha256":"2ad41717a4125c0229550237961bc89e1e511704838fb7ac6b31d4e26f3e24a7"},"schema_version":"1.0","source":{"id":"1801.02218","kind":"arxiv","version":1}},"canonical_sha256":"cf7e2cb8f20cf4647b2f2118b3ec0476768437c70426812f5194d5d4a9076d1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf7e2cb8f20cf4647b2f2118b3ec0476768437c70426812f5194d5d4a9076d1e","first_computed_at":"2026-05-18T00:26:34.519215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:34.519215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HeK515DKQ5mkdkGsgJSzmJicm/mOYWqb3nZIc5mBxmQqZb595A5hsqIiVY7jIs1ECKa6AOhRxm3uX0t8d38lDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:34.519899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.02218","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46c41e7b4182bda7f8b88b67786bf9797d889a5110c9adbf1c08c43332979442","sha256:a871bc88c8742c77c2659aabb24b9dfa6f89f7b4b7577e951f14478805d67772"],"state_sha256":"cdc1d4dd9dcc3eca25aa59d325fcf8f51a90be6c3e6aa4266166391c44fc05cb"}