{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:S2LD7M56ZHV3DBFIMUKIVY7DHY","short_pith_number":"pith:S2LD7M56","schema_version":"1.0","canonical_sha256":"96963fb3bec9ebb184a865148ae3e33e3b21627cd030866e1e999da4e1f5844c","source":{"kind":"arxiv","id":"2410.23874","version":1},"attestation_state":"computed","paper":{"title":"Optimization over convex polyhedra via Hadamard parametrizations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kim-Chuan Toh, Tianyun Tang","submitted_at":"2024-10-31T12:34:59Z","abstract_excerpt":"In this paper, we study linearly constrained optimization problems (LCP). After applying Hadamard parametrization, the feasible set of the parametrized problem (LCPH) becomes an algebraic variety, with conducive geometric properties which we explore in depth. We derive explicit formulas for the tangent cones and second-order tangent sets associated with the parametrized polyhedra. Based on these formulas, we develop a procedure to recover the Lagrangian multipliers associated with the constraints to verify the optimality conditions of the given primal variable without requiring additional cons"},"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":"2410.23874","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-31T12:34:59Z","cross_cats_sorted":[],"title_canon_sha256":"4631635e2c08a4d04ea8e7f280998520afc124179890c06ec7d71fc81895ba1f","abstract_canon_sha256":"eb77feb4fe8a44d89c49d8d73dbe17d40630285923358117a544d004d3686c37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:29:06.620218Z","signature_b64":"s+YPojZhr0JdCUnTBOIoHK6kQ66GDplZUxJe5tFdZOk6uAyw2WAhRcvyBIQeI70yXrorU70Tje9oh7ufuEQoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96963fb3bec9ebb184a865148ae3e33e3b21627cd030866e1e999da4e1f5844c","last_reissued_at":"2026-07-05T09:29:06.619623Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:29:06.619623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimization over convex polyhedra via Hadamard parametrizations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kim-Chuan Toh, Tianyun Tang","submitted_at":"2024-10-31T12:34:59Z","abstract_excerpt":"In this paper, we study linearly constrained optimization problems (LCP). After applying Hadamard parametrization, the feasible set of the parametrized problem (LCPH) becomes an algebraic variety, with conducive geometric properties which we explore in depth. We derive explicit formulas for the tangent cones and second-order tangent sets associated with the parametrized polyhedra. Based on these formulas, we develop a procedure to recover the Lagrangian multipliers associated with the constraints to verify the optimality conditions of the given primal variable without requiring additional cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.23874","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.23874/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2410.23874","created_at":"2026-07-05T09:29:06.619703+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.23874v1","created_at":"2026-07-05T09:29:06.619703+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.23874","created_at":"2026-07-05T09:29:06.619703+00:00"},{"alias_kind":"pith_short_12","alias_value":"S2LD7M56ZHV3","created_at":"2026-07-05T09:29:06.619703+00:00"},{"alias_kind":"pith_short_16","alias_value":"S2LD7M56ZHV3DBFI","created_at":"2026-07-05T09:29:06.619703+00:00"},{"alias_kind":"pith_short_8","alias_value":"S2LD7M56","created_at":"2026-07-05T09:29:06.619703+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/S2LD7M56ZHV3DBFIMUKIVY7DHY","json":"https://pith.science/pith/S2LD7M56ZHV3DBFIMUKIVY7DHY.json","graph_json":"https://pith.science/api/pith-number/S2LD7M56ZHV3DBFIMUKIVY7DHY/graph.json","events_json":"https://pith.science/api/pith-number/S2LD7M56ZHV3DBFIMUKIVY7DHY/events.json","paper":"https://pith.science/paper/S2LD7M56"},"agent_actions":{"view_html":"https://pith.science/pith/S2LD7M56ZHV3DBFIMUKIVY7DHY","download_json":"https://pith.science/pith/S2LD7M56ZHV3DBFIMUKIVY7DHY.json","view_paper":"https://pith.science/paper/S2LD7M56","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.23874&json=true","fetch_graph":"https://pith.science/api/pith-number/S2LD7M56ZHV3DBFIMUKIVY7DHY/graph.json","fetch_events":"https://pith.science/api/pith-number/S2LD7M56ZHV3DBFIMUKIVY7DHY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S2LD7M56ZHV3DBFIMUKIVY7DHY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S2LD7M56ZHV3DBFIMUKIVY7DHY/action/storage_attestation","attest_author":"https://pith.science/pith/S2LD7M56ZHV3DBFIMUKIVY7DHY/action/author_attestation","sign_citation":"https://pith.science/pith/S2LD7M56ZHV3DBFIMUKIVY7DHY/action/citation_signature","submit_replication":"https://pith.science/pith/S2LD7M56ZHV3DBFIMUKIVY7DHY/action/replication_record"}},"created_at":"2026-07-05T09:29:06.619703+00:00","updated_at":"2026-07-05T09:29:06.619703+00:00"}