{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:4FBOJ3OOPO7IAJU3J6GIMWN3AS","short_pith_number":"pith:4FBOJ3OO","schema_version":"1.0","canonical_sha256":"e142e4edce7bbe80269b4f8c8659bb049b70068f5539449282a63693cfc3d491","source":{"kind":"arxiv","id":"2502.13849","version":1},"attestation_state":"computed","paper":{"title":"A low-rank augmented Lagrangian method for doubly nonnegative relaxations of mixed-binary quadratic programs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Di Hou, Kim-Chuan Toh, Tianyun Tang","submitted_at":"2025-02-19T16:12:14Z","abstract_excerpt":"Doubly nonnegative (DNN) programming problems are known to be challenging to solve because of their huge number of $\\Omega(n^2)$ constraints and $\\Omega(n^2)$ variables. In this work, we introduce RNNAL, a method for solving DNN relaxations of large-scale mixed-binary quadratic programs by leveraging their solutions' possible low-rank property. RNNAL is a globally convergent Riemannian augmented Lagrangian method (ALM) that penalizes the nonnegativity and complementarity constraints while preserving all other constraints as an algebraic variety. After applying the low-rank decomposition to the"},"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":"2502.13849","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-02-19T16:12:14Z","cross_cats_sorted":[],"title_canon_sha256":"1d5ce022851e937cc81647b1b57643cc2144c95afc7c88219b937edaf8a36bc8","abstract_canon_sha256":"406a16f91701391f52ce222354db0568d6b01a520145d07629af812e2155f334"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:17:01.430571Z","signature_b64":"FqjmFb29Xfuo2OZox7w8M4pEChWeJ/I7PhMK0gJLCfGoPUntA12ERs3IlH4zrMZqryi7QN7YyobqlyDfhjmmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e142e4edce7bbe80269b4f8c8659bb049b70068f5539449282a63693cfc3d491","last_reissued_at":"2026-07-05T10:17:01.430096Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:17:01.430096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A low-rank augmented Lagrangian method for doubly nonnegative relaxations of mixed-binary quadratic programs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Di Hou, Kim-Chuan Toh, Tianyun Tang","submitted_at":"2025-02-19T16:12:14Z","abstract_excerpt":"Doubly nonnegative (DNN) programming problems are known to be challenging to solve because of their huge number of $\\Omega(n^2)$ constraints and $\\Omega(n^2)$ variables. In this work, we introduce RNNAL, a method for solving DNN relaxations of large-scale mixed-binary quadratic programs by leveraging their solutions' possible low-rank property. RNNAL is a globally convergent Riemannian augmented Lagrangian method (ALM) that penalizes the nonnegativity and complementarity constraints while preserving all other constraints as an algebraic variety. After applying the low-rank decomposition to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.13849","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/2502.13849/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":"2502.13849","created_at":"2026-07-05T10:17:01.430152+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.13849v1","created_at":"2026-07-05T10:17:01.430152+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.13849","created_at":"2026-07-05T10:17:01.430152+00:00"},{"alias_kind":"pith_short_12","alias_value":"4FBOJ3OOPO7I","created_at":"2026-07-05T10:17:01.430152+00:00"},{"alias_kind":"pith_short_16","alias_value":"4FBOJ3OOPO7IAJU3","created_at":"2026-07-05T10:17:01.430152+00:00"},{"alias_kind":"pith_short_8","alias_value":"4FBOJ3OO","created_at":"2026-07-05T10:17:01.430152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.13776","citing_title":"RiNNAL+: a Riemannian ALM Solver for SDP-RLT Relaxations of Mixed-Binary Quadratic Programs","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4FBOJ3OOPO7IAJU3J6GIMWN3AS","json":"https://pith.science/pith/4FBOJ3OOPO7IAJU3J6GIMWN3AS.json","graph_json":"https://pith.science/api/pith-number/4FBOJ3OOPO7IAJU3J6GIMWN3AS/graph.json","events_json":"https://pith.science/api/pith-number/4FBOJ3OOPO7IAJU3J6GIMWN3AS/events.json","paper":"https://pith.science/paper/4FBOJ3OO"},"agent_actions":{"view_html":"https://pith.science/pith/4FBOJ3OOPO7IAJU3J6GIMWN3AS","download_json":"https://pith.science/pith/4FBOJ3OOPO7IAJU3J6GIMWN3AS.json","view_paper":"https://pith.science/paper/4FBOJ3OO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.13849&json=true","fetch_graph":"https://pith.science/api/pith-number/4FBOJ3OOPO7IAJU3J6GIMWN3AS/graph.json","fetch_events":"https://pith.science/api/pith-number/4FBOJ3OOPO7IAJU3J6GIMWN3AS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4FBOJ3OOPO7IAJU3J6GIMWN3AS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4FBOJ3OOPO7IAJU3J6GIMWN3AS/action/storage_attestation","attest_author":"https://pith.science/pith/4FBOJ3OOPO7IAJU3J6GIMWN3AS/action/author_attestation","sign_citation":"https://pith.science/pith/4FBOJ3OOPO7IAJU3J6GIMWN3AS/action/citation_signature","submit_replication":"https://pith.science/pith/4FBOJ3OOPO7IAJU3J6GIMWN3AS/action/replication_record"}},"created_at":"2026-07-05T10:17:01.430152+00:00","updated_at":"2026-07-05T10:17:01.430152+00:00"}