{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:MH6TDYTCNZK7WHNO7PV2BBV7EP","short_pith_number":"pith:MH6TDYTC","schema_version":"1.0","canonical_sha256":"61fd31e2626e55fb1daefbeba086bf23c9f6b1bf09449dedb0df9bf3920db238","source":{"kind":"arxiv","id":"2409.04671","version":1},"attestation_state":"computed","paper":{"title":"Decomposition-Invariant Pairwise Frank-Wolfe Algorithm for Constrained Multiobjective Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Liping Tang, Zhuoxin Fan","submitted_at":"2024-09-07T01:26:48Z","abstract_excerpt":"Recently the away-step Frank-Wolfe algoritm for constrained multiobjective optimization has been shown linear convergence rate over a polytope which is generated by finite points set. In this paper we design a decomposition-invariant pairwise frank-wolfe algorithm for multiobjective optimization that the feasible region is an arbitrary bounded polytope. We prove it has linear convergence rate of the whole sequence to a pareto optimal solution under strongly convexity without other assumptions."},"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":"2409.04671","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-09-07T01:26:48Z","cross_cats_sorted":[],"title_canon_sha256":"7ca7032ed1996d4f970a909d63857d380059037ecbebb572c7afa54aec23221d","abstract_canon_sha256":"9ad539409fa93b5c43614594b464962fbfec3438209b18555fab8edd5acaa6bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:04:16.150000Z","signature_b64":"bSo1wCfHARNzApFmGmVVk6Ppr4634XA3WRvX/Xm+K0hl89AxWDmjDvqMa3OxU6ZIiOxyOw1yqlf7vH3Tx386Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61fd31e2626e55fb1daefbeba086bf23c9f6b1bf09449dedb0df9bf3920db238","last_reissued_at":"2026-07-05T09:04:16.149627Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:04:16.149627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decomposition-Invariant Pairwise Frank-Wolfe Algorithm for Constrained Multiobjective Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Liping Tang, Zhuoxin Fan","submitted_at":"2024-09-07T01:26:48Z","abstract_excerpt":"Recently the away-step Frank-Wolfe algoritm for constrained multiobjective optimization has been shown linear convergence rate over a polytope which is generated by finite points set. In this paper we design a decomposition-invariant pairwise frank-wolfe algorithm for multiobjective optimization that the feasible region is an arbitrary bounded polytope. We prove it has linear convergence rate of the whole sequence to a pareto optimal solution under strongly convexity without other assumptions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.04671","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/2409.04671/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":"2409.04671","created_at":"2026-07-05T09:04:16.149683+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.04671v1","created_at":"2026-07-05T09:04:16.149683+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.04671","created_at":"2026-07-05T09:04:16.149683+00:00"},{"alias_kind":"pith_short_12","alias_value":"MH6TDYTCNZK7","created_at":"2026-07-05T09:04:16.149683+00:00"},{"alias_kind":"pith_short_16","alias_value":"MH6TDYTCNZK7WHNO","created_at":"2026-07-05T09:04:16.149683+00:00"},{"alias_kind":"pith_short_8","alias_value":"MH6TDYTC","created_at":"2026-07-05T09:04:16.149683+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/MH6TDYTCNZK7WHNO7PV2BBV7EP","json":"https://pith.science/pith/MH6TDYTCNZK7WHNO7PV2BBV7EP.json","graph_json":"https://pith.science/api/pith-number/MH6TDYTCNZK7WHNO7PV2BBV7EP/graph.json","events_json":"https://pith.science/api/pith-number/MH6TDYTCNZK7WHNO7PV2BBV7EP/events.json","paper":"https://pith.science/paper/MH6TDYTC"},"agent_actions":{"view_html":"https://pith.science/pith/MH6TDYTCNZK7WHNO7PV2BBV7EP","download_json":"https://pith.science/pith/MH6TDYTCNZK7WHNO7PV2BBV7EP.json","view_paper":"https://pith.science/paper/MH6TDYTC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.04671&json=true","fetch_graph":"https://pith.science/api/pith-number/MH6TDYTCNZK7WHNO7PV2BBV7EP/graph.json","fetch_events":"https://pith.science/api/pith-number/MH6TDYTCNZK7WHNO7PV2BBV7EP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MH6TDYTCNZK7WHNO7PV2BBV7EP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MH6TDYTCNZK7WHNO7PV2BBV7EP/action/storage_attestation","attest_author":"https://pith.science/pith/MH6TDYTCNZK7WHNO7PV2BBV7EP/action/author_attestation","sign_citation":"https://pith.science/pith/MH6TDYTCNZK7WHNO7PV2BBV7EP/action/citation_signature","submit_replication":"https://pith.science/pith/MH6TDYTCNZK7WHNO7PV2BBV7EP/action/replication_record"}},"created_at":"2026-07-05T09:04:16.149683+00:00","updated_at":"2026-07-05T09:04:16.149683+00:00"}