{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:UINSFJEJBPGR2ZOWRRY6KWURVC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0c7f98ae4c0379dc77d5cb69caacfa58970fb6a034f0c5976f9527b06edc96d5","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-11-20T10:37:26Z","title_canon_sha256":"9cf955a7d2382c2b8bd1cf83d928b9c383e78bbb74d9113b02579554e9ac6f38"},"schema_version":"1.0","source":{"id":"2211.10942","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.10942","created_at":"2026-07-05T05:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"2211.10942v1","created_at":"2026-07-05T05:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.10942","created_at":"2026-07-05T05:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"UINSFJEJBPGR","created_at":"2026-07-05T05:17:36Z"},{"alias_kind":"pith_short_16","alias_value":"UINSFJEJBPGR2ZOW","created_at":"2026-07-05T05:17:36Z"},{"alias_kind":"pith_short_8","alias_value":"UINSFJEJ","created_at":"2026-07-05T05:17:36Z"}],"graph_snapshots":[{"event_id":"sha256:51345b9d933e945a8477c5148d179f0baa9b83508d7463962000e73f9d11cee5","target":"graph","created_at":"2026-07-05T05:17:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2211.10942/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we propose a clean and general proof framework to establish the convergence analysis of the Difference-of-Convex (DC) programming algorithm (DCA) for both standard DC program and convex constrained DC program. We first discuss suitable assumptions for the well-definiteness of DCA. Then, we focus on the convergence analysis of DCA, in particular, the global convergence of the sequence $\\{x^k\\}$ generated by DCA under the Lojasiewicz subgradient inequality and the Kurdyka-Lojasiewicz property respectively. Moreover, the convergence rate for the sequences $\\{f(x^k)\\}$ and $\\{\\|x^k-","authors_text":"Yi-Shuai Niu","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-11-20T10:37:26Z","title":"On the convergence analysis of DCA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.10942","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bb7c6a8133652e08b9c9da78d6394bbb702d157a89c5b058d50d27b0263ad53b","target":"record","created_at":"2026-07-05T05:17:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0c7f98ae4c0379dc77d5cb69caacfa58970fb6a034f0c5976f9527b06edc96d5","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-11-20T10:37:26Z","title_canon_sha256":"9cf955a7d2382c2b8bd1cf83d928b9c383e78bbb74d9113b02579554e9ac6f38"},"schema_version":"1.0","source":{"id":"2211.10942","kind":"arxiv","version":1}},"canonical_sha256":"a21b22a4890bcd1d65d68c71e55a91a8992556ec2ae5139bd5ff6dd5fd7b774d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a21b22a4890bcd1d65d68c71e55a91a8992556ec2ae5139bd5ff6dd5fd7b774d","first_computed_at":"2026-07-05T05:17:36.759583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:17:36.759583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vZ0LNTzlhRIl9wQd92c5MnJNMLc4vRFQPEaImZZXb0ogWcNeNyuOsiROIoaA6GYQDQ2+qEdBgKVtKWpTvIuwCA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:17:36.759957Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.10942","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb7c6a8133652e08b9c9da78d6394bbb702d157a89c5b058d50d27b0263ad53b","sha256:51345b9d933e945a8477c5148d179f0baa9b83508d7463962000e73f9d11cee5"],"state_sha256":"071ac6bef3a9936a923469ebd4bdf33638c864985266d64650adb83462a6adec"}