{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:QQQPJZLNDHWHAZ4FLIFHF3IC34","short_pith_number":"pith:QQQPJZLN","schema_version":"1.0","canonical_sha256":"8420f4e56d19ec7067855a0a72ed02df0eecb064d6fa78b0972c9c92e8f0b3dc","source":{"kind":"arxiv","id":"2406.05740","version":2},"attestation_state":"computed","paper":{"title":"Convergence of ZH-type nonmonotone descent method for Kurdyka-{\\L}ojasiewicz optimization problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Houduo Qi, Shaohua Pan, Ting Tao, Yitian Qian","submitted_at":"2024-06-09T11:13:25Z","abstract_excerpt":"We propose a novel iterative framework for minimizing a proper lower semicontinuous Kurdyka-{\\L}ojasiewicz (KL) function $\\Phi$. It comprises a Zhang-Hager (ZH-type) nonmonotone decrease condition and a relative error condition. Hence, the sequence generated by the ZH-type nonmonotone descent methods will fall within this framework. Any sequence conforming to this framework is proved to converge to a critical point of $\\Phi$. If in addition $\\Phi$ has the KL property of exponent $\\theta\\!\\in(0,1)$ at the critical point, the convergence has a linear rate for $\\theta\\in(0,1/2]$ and a sublinear r"},"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":"2406.05740","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-06-09T11:13:25Z","cross_cats_sorted":[],"title_canon_sha256":"0c81f50585ef9d3708d930ab498c2ee935d74e84e60612bb1684db8aec1a5a1e","abstract_canon_sha256":"998570816a94d4ff963a904a61b7a2bfcd4d8f9e7ec94d5b62cf82b858b84254"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:44:10.075272Z","signature_b64":"9czuSKGuKlwrcjBrVOxh/+dfuI9Ym+etzCu8CxfcKQszSIl6dNq3EKwmHMKHxV4rDV0fKJ7FZQ1+YXlEHfmmDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8420f4e56d19ec7067855a0a72ed02df0eecb064d6fa78b0972c9c92e8f0b3dc","last_reissued_at":"2026-07-05T09:44:10.074787Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:44:10.074787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence of ZH-type nonmonotone descent method for Kurdyka-{\\L}ojasiewicz optimization problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Houduo Qi, Shaohua Pan, Ting Tao, Yitian Qian","submitted_at":"2024-06-09T11:13:25Z","abstract_excerpt":"We propose a novel iterative framework for minimizing a proper lower semicontinuous Kurdyka-{\\L}ojasiewicz (KL) function $\\Phi$. It comprises a Zhang-Hager (ZH-type) nonmonotone decrease condition and a relative error condition. Hence, the sequence generated by the ZH-type nonmonotone descent methods will fall within this framework. Any sequence conforming to this framework is proved to converge to a critical point of $\\Phi$. If in addition $\\Phi$ has the KL property of exponent $\\theta\\!\\in(0,1)$ at the critical point, the convergence has a linear rate for $\\theta\\in(0,1/2]$ and a sublinear r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.05740","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/2406.05740/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":"2406.05740","created_at":"2026-07-05T09:44:10.074841+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.05740v2","created_at":"2026-07-05T09:44:10.074841+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.05740","created_at":"2026-07-05T09:44:10.074841+00:00"},{"alias_kind":"pith_short_12","alias_value":"QQQPJZLNDHWH","created_at":"2026-07-05T09:44:10.074841+00:00"},{"alias_kind":"pith_short_16","alias_value":"QQQPJZLNDHWHAZ4F","created_at":"2026-07-05T09:44:10.074841+00:00"},{"alias_kind":"pith_short_8","alias_value":"QQQPJZLN","created_at":"2026-07-05T09:44:10.074841+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.19256","citing_title":"Convergence analysis of nonmonotone proximal gradient methods under local Lipschitz continuity and Kurdyka--{\\L}ojasiewicz property","ref_index":27,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QQQPJZLNDHWHAZ4FLIFHF3IC34","json":"https://pith.science/pith/QQQPJZLNDHWHAZ4FLIFHF3IC34.json","graph_json":"https://pith.science/api/pith-number/QQQPJZLNDHWHAZ4FLIFHF3IC34/graph.json","events_json":"https://pith.science/api/pith-number/QQQPJZLNDHWHAZ4FLIFHF3IC34/events.json","paper":"https://pith.science/paper/QQQPJZLN"},"agent_actions":{"view_html":"https://pith.science/pith/QQQPJZLNDHWHAZ4FLIFHF3IC34","download_json":"https://pith.science/pith/QQQPJZLNDHWHAZ4FLIFHF3IC34.json","view_paper":"https://pith.science/paper/QQQPJZLN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.05740&json=true","fetch_graph":"https://pith.science/api/pith-number/QQQPJZLNDHWHAZ4FLIFHF3IC34/graph.json","fetch_events":"https://pith.science/api/pith-number/QQQPJZLNDHWHAZ4FLIFHF3IC34/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QQQPJZLNDHWHAZ4FLIFHF3IC34/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QQQPJZLNDHWHAZ4FLIFHF3IC34/action/storage_attestation","attest_author":"https://pith.science/pith/QQQPJZLNDHWHAZ4FLIFHF3IC34/action/author_attestation","sign_citation":"https://pith.science/pith/QQQPJZLNDHWHAZ4FLIFHF3IC34/action/citation_signature","submit_replication":"https://pith.science/pith/QQQPJZLNDHWHAZ4FLIFHF3IC34/action/replication_record"}},"created_at":"2026-07-05T09:44:10.074841+00:00","updated_at":"2026-07-05T09:44:10.074841+00:00"}