{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:LHRSOIWPYMY3C7QMZY2OCZGXDC","short_pith_number":"pith:LHRSOIWP","schema_version":"1.0","canonical_sha256":"59e32722cfc331b17e0cce34e164d7188898eb5ab9aeedab6812a2d986b43b4c","source":{"kind":"arxiv","id":"2405.08485","version":2},"attestation_state":"computed","paper":{"title":"Doubly relaxed forward-Douglas--Rachford splitting for the sum of two nonconvex and a DC function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Minh N. Dao, Phan Thanh Tung, Tan Nhat Pham","submitted_at":"2024-05-14T10:18:38Z","abstract_excerpt":"In this paper, we consider a class of structured nonconvex nonsmooth optimization problems whose objective function is the sum of three nonconvex functions, one of which is expressed in a difference-of-convex (DC) form. This problem class covers several important structures in the literature including the sum of three functions and the general DC program. We propose a splitting algorithm and prove the subsequential convergence to a stationary point of the problem. The full sequential convergence, along with convergence rates for both the iterates and objective function values, is then establis"},"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":"2405.08485","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-05-14T10:18:38Z","cross_cats_sorted":[],"title_canon_sha256":"cf8aa43a7b6228646246b67a9577a17b973b067c9c97de67e6c323843e96bd9f","abstract_canon_sha256":"c5743c85dc6f43df91750df493be1a54cc3822135ec6f095b68e4ad3ae6feb19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:12.249207Z","signature_b64":"J5fzMF8/UwOKeJ7qYEo7B9s6fboQZB0F9dDFNIeIF+omdSi0NamswizM/2UqEiIMiGrF2PssWc1PKt5+7AGfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59e32722cfc331b17e0cce34e164d7188898eb5ab9aeedab6812a2d986b43b4c","last_reissued_at":"2026-07-05T11:18:12.248656Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:12.248656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Doubly relaxed forward-Douglas--Rachford splitting for the sum of two nonconvex and a DC function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Minh N. Dao, Phan Thanh Tung, Tan Nhat Pham","submitted_at":"2024-05-14T10:18:38Z","abstract_excerpt":"In this paper, we consider a class of structured nonconvex nonsmooth optimization problems whose objective function is the sum of three nonconvex functions, one of which is expressed in a difference-of-convex (DC) form. This problem class covers several important structures in the literature including the sum of three functions and the general DC program. We propose a splitting algorithm and prove the subsequential convergence to a stationary point of the problem. The full sequential convergence, along with convergence rates for both the iterates and objective function values, is then establis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.08485","kind":"arxiv","version":2},"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/2405.08485/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":"2405.08485","created_at":"2026-07-05T11:18:12.248732+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.08485v2","created_at":"2026-07-05T11:18:12.248732+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.08485","created_at":"2026-07-05T11:18:12.248732+00:00"},{"alias_kind":"pith_short_12","alias_value":"LHRSOIWPYMY3","created_at":"2026-07-05T11:18:12.248732+00:00"},{"alias_kind":"pith_short_16","alias_value":"LHRSOIWPYMY3C7QM","created_at":"2026-07-05T11:18:12.248732+00:00"},{"alias_kind":"pith_short_8","alias_value":"LHRSOIWP","created_at":"2026-07-05T11:18:12.248732+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.04889","citing_title":"Projected proximal gradient trust-region algorithm for nonsmooth optimization","ref_index":20,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LHRSOIWPYMY3C7QMZY2OCZGXDC","json":"https://pith.science/pith/LHRSOIWPYMY3C7QMZY2OCZGXDC.json","graph_json":"https://pith.science/api/pith-number/LHRSOIWPYMY3C7QMZY2OCZGXDC/graph.json","events_json":"https://pith.science/api/pith-number/LHRSOIWPYMY3C7QMZY2OCZGXDC/events.json","paper":"https://pith.science/paper/LHRSOIWP"},"agent_actions":{"view_html":"https://pith.science/pith/LHRSOIWPYMY3C7QMZY2OCZGXDC","download_json":"https://pith.science/pith/LHRSOIWPYMY3C7QMZY2OCZGXDC.json","view_paper":"https://pith.science/paper/LHRSOIWP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.08485&json=true","fetch_graph":"https://pith.science/api/pith-number/LHRSOIWPYMY3C7QMZY2OCZGXDC/graph.json","fetch_events":"https://pith.science/api/pith-number/LHRSOIWPYMY3C7QMZY2OCZGXDC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LHRSOIWPYMY3C7QMZY2OCZGXDC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LHRSOIWPYMY3C7QMZY2OCZGXDC/action/storage_attestation","attest_author":"https://pith.science/pith/LHRSOIWPYMY3C7QMZY2OCZGXDC/action/author_attestation","sign_citation":"https://pith.science/pith/LHRSOIWPYMY3C7QMZY2OCZGXDC/action/citation_signature","submit_replication":"https://pith.science/pith/LHRSOIWPYMY3C7QMZY2OCZGXDC/action/replication_record"}},"created_at":"2026-07-05T11:18:12.248732+00:00","updated_at":"2026-07-05T11:18:12.248732+00:00"}