{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GWCX2S564C7AKLFLN6A5F5AUIF","short_pith_number":"pith:GWCX2S56","schema_version":"1.0","canonical_sha256":"35857d4bbee0be052cab6f81d2f4144178a095fa257772f149e0b23c46c5a424","source":{"kind":"arxiv","id":"1509.01156","version":1},"attestation_state":"computed","paper":{"title":"Bernstein Polynomial Relaxations for Polynomial Optimization Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Mohamed Amin Ben Sassi, Sriram Sankaranarayanan","submitted_at":"2015-09-03T16:51:34Z","abstract_excerpt":"In this paper, we examine linear programming (LP) relaxations based on Bernstein polynomials for polynomial optimization problems (POPs). We present a progression of increasingly more precise LP relaxations based on expressing the given polynomial in its Bernstein form, as a linear combination of Bernstein polynomials. The well-known bounds on Bernstein polynomials over the unit box combined with linear inter-relationships between Bernstein polynomials help us formulate \"Bernstein inequalities\" which yield tighter lower bounds for POPs in bounded rectangular domains. The results can be easily "},"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":"1509.01156","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-03T16:51:34Z","cross_cats_sorted":[],"title_canon_sha256":"94a6885b785243fc77247aed05a94c8a12da4a87faded9f2cf6cf0b9c99ccff4","abstract_canon_sha256":"13c71bd676208c737754d7411886ea09a8103b8114a91f1455be56ba5f00db5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:04.203066Z","signature_b64":"85pa/xZpuIzgkzUHluwV8OC5oqsGTNX+iPr2wKbsosGLeq7zbYZpnt2o01DxOhVkna1ix6DjQzKJgJzwBGQ4BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35857d4bbee0be052cab6f81d2f4144178a095fa257772f149e0b23c46c5a424","last_reissued_at":"2026-05-18T01:34:04.202492Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:04.202492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bernstein Polynomial Relaxations for Polynomial Optimization Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Mohamed Amin Ben Sassi, Sriram Sankaranarayanan","submitted_at":"2015-09-03T16:51:34Z","abstract_excerpt":"In this paper, we examine linear programming (LP) relaxations based on Bernstein polynomials for polynomial optimization problems (POPs). We present a progression of increasingly more precise LP relaxations based on expressing the given polynomial in its Bernstein form, as a linear combination of Bernstein polynomials. The well-known bounds on Bernstein polynomials over the unit box combined with linear inter-relationships between Bernstein polynomials help us formulate \"Bernstein inequalities\" which yield tighter lower bounds for POPs in bounded rectangular domains. The results can be easily "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01156","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":""},"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":"1509.01156","created_at":"2026-05-18T01:34:04.202586+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.01156v1","created_at":"2026-05-18T01:34:04.202586+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01156","created_at":"2026-05-18T01:34:04.202586+00:00"},{"alias_kind":"pith_short_12","alias_value":"GWCX2S564C7A","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GWCX2S564C7AKLFL","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GWCX2S56","created_at":"2026-05-18T12:29:22.688609+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/GWCX2S564C7AKLFLN6A5F5AUIF","json":"https://pith.science/pith/GWCX2S564C7AKLFLN6A5F5AUIF.json","graph_json":"https://pith.science/api/pith-number/GWCX2S564C7AKLFLN6A5F5AUIF/graph.json","events_json":"https://pith.science/api/pith-number/GWCX2S564C7AKLFLN6A5F5AUIF/events.json","paper":"https://pith.science/paper/GWCX2S56"},"agent_actions":{"view_html":"https://pith.science/pith/GWCX2S564C7AKLFLN6A5F5AUIF","download_json":"https://pith.science/pith/GWCX2S564C7AKLFLN6A5F5AUIF.json","view_paper":"https://pith.science/paper/GWCX2S56","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.01156&json=true","fetch_graph":"https://pith.science/api/pith-number/GWCX2S564C7AKLFLN6A5F5AUIF/graph.json","fetch_events":"https://pith.science/api/pith-number/GWCX2S564C7AKLFLN6A5F5AUIF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GWCX2S564C7AKLFLN6A5F5AUIF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GWCX2S564C7AKLFLN6A5F5AUIF/action/storage_attestation","attest_author":"https://pith.science/pith/GWCX2S564C7AKLFLN6A5F5AUIF/action/author_attestation","sign_citation":"https://pith.science/pith/GWCX2S564C7AKLFLN6A5F5AUIF/action/citation_signature","submit_replication":"https://pith.science/pith/GWCX2S564C7AKLFLN6A5F5AUIF/action/replication_record"}},"created_at":"2026-05-18T01:34:04.202586+00:00","updated_at":"2026-05-18T01:34:04.202586+00:00"}