{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:Q2ONPHMGV5MBN7ZYBFGEZ5BMPT","short_pith_number":"pith:Q2ONPHMG","schema_version":"1.0","canonical_sha256":"869cd79d86af5816ff38094c4cf42c7ce99d5445fec35ae43e9016bf64af192f","source":{"kind":"arxiv","id":"1401.0081","version":1},"attestation_state":"computed","paper":{"title":"A new semidefinite relaxation for $\\ell_{1}$-constrained quadratic optimization and extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Sheng-Nan Han, Yong Xia, Yu-Jun Gong","submitted_at":"2013-12-31T03:38:39Z","abstract_excerpt":"In this paper, by improving the variable-splitting approach, we propose a new semidefinite programming (SDP) relaxation for the nonconvex quadratic optimization problem over the $\\ell_1$ unit ball (QPL1). It dominates the state-of-the-art SDP-based bound for (QPL1). As extensions, we apply the new approach to the relaxation problem of the sparse principal component analysis and the nonconvex quadratic optimization problem over the $\\ell_p$ ($1< p<2$) unit ball and then show the dominance of the new relaxation."},"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":"1401.0081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-12-31T03:38:39Z","cross_cats_sorted":[],"title_canon_sha256":"2f572b05135252cca4ebdd8767363656627b9999bf5382ce49333afa84cd18a7","abstract_canon_sha256":"9bdb765a015e9a511f4d03ff2d6d394bd092324b788e86966f71bbefb14d43a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:31.143932Z","signature_b64":"Kg0hmRsie23tFCvWmbDmjEIHBwy5edJl/avlWkpuhWtPz8PwqFu74zgIsnSmG2ZupatgyywQaf/7B0dFgfErCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"869cd79d86af5816ff38094c4cf42c7ce99d5445fec35ae43e9016bf64af192f","last_reissued_at":"2026-05-18T03:03:31.143061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:31.143061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new semidefinite relaxation for $\\ell_{1}$-constrained quadratic optimization and extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Sheng-Nan Han, Yong Xia, Yu-Jun Gong","submitted_at":"2013-12-31T03:38:39Z","abstract_excerpt":"In this paper, by improving the variable-splitting approach, we propose a new semidefinite programming (SDP) relaxation for the nonconvex quadratic optimization problem over the $\\ell_1$ unit ball (QPL1). It dominates the state-of-the-art SDP-based bound for (QPL1). As extensions, we apply the new approach to the relaxation problem of the sparse principal component analysis and the nonconvex quadratic optimization problem over the $\\ell_p$ ($1< p<2$) unit ball and then show the dominance of the new relaxation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0081","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":"1401.0081","created_at":"2026-05-18T03:03:31.143228+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.0081v1","created_at":"2026-05-18T03:03:31.143228+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0081","created_at":"2026-05-18T03:03:31.143228+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q2ONPHMGV5MB","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q2ONPHMGV5MBN7ZY","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q2ONPHMG","created_at":"2026-05-18T12:27:57.521954+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/Q2ONPHMGV5MBN7ZYBFGEZ5BMPT","json":"https://pith.science/pith/Q2ONPHMGV5MBN7ZYBFGEZ5BMPT.json","graph_json":"https://pith.science/api/pith-number/Q2ONPHMGV5MBN7ZYBFGEZ5BMPT/graph.json","events_json":"https://pith.science/api/pith-number/Q2ONPHMGV5MBN7ZYBFGEZ5BMPT/events.json","paper":"https://pith.science/paper/Q2ONPHMG"},"agent_actions":{"view_html":"https://pith.science/pith/Q2ONPHMGV5MBN7ZYBFGEZ5BMPT","download_json":"https://pith.science/pith/Q2ONPHMGV5MBN7ZYBFGEZ5BMPT.json","view_paper":"https://pith.science/paper/Q2ONPHMG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.0081&json=true","fetch_graph":"https://pith.science/api/pith-number/Q2ONPHMGV5MBN7ZYBFGEZ5BMPT/graph.json","fetch_events":"https://pith.science/api/pith-number/Q2ONPHMGV5MBN7ZYBFGEZ5BMPT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q2ONPHMGV5MBN7ZYBFGEZ5BMPT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q2ONPHMGV5MBN7ZYBFGEZ5BMPT/action/storage_attestation","attest_author":"https://pith.science/pith/Q2ONPHMGV5MBN7ZYBFGEZ5BMPT/action/author_attestation","sign_citation":"https://pith.science/pith/Q2ONPHMGV5MBN7ZYBFGEZ5BMPT/action/citation_signature","submit_replication":"https://pith.science/pith/Q2ONPHMGV5MBN7ZYBFGEZ5BMPT/action/replication_record"}},"created_at":"2026-05-18T03:03:31.143228+00:00","updated_at":"2026-05-18T03:03:31.143228+00:00"}