{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VDKB4CABCZR4Q3YC275L62VXPL","short_pith_number":"pith:VDKB4CAB","schema_version":"1.0","canonical_sha256":"a8d41e08011663c86f02d7fabf6ab77af65bab70bbf4c86aeffdf87b9673d385","source":{"kind":"arxiv","id":"1512.09302","version":2},"attestation_state":"computed","paper":{"title":"Linear Convergence of Proximal Gradient Algorithm with Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.OC","authors_text":"Bo Wen, Ting Kei Pong, Xiaojun Chen","submitted_at":"2015-12-31T14:57:03Z","abstract_excerpt":"In this paper, we study the proximal gradient algorithm with extrapolation for minimizing the sum of a Lipschitz differentiable function and a proper closed convex function. Under the error bound condition used in [19] for analyzing the convergence of the proximal gradient algorithm, we show that there exists a threshold such that if the extrapolation coefficients are chosen below this threshold, then the sequence generated converges $R$-linearly to a stationary point of the problem. Moreover, the corresponding sequence of objective values is also $R$-linearly convergent. In addition, the thre"},"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":"1512.09302","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-31T14:57:03Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"1c441539fd85722a676a5c035effb3b19c84c20aea1755142c62851c03a793a9","abstract_canon_sha256":"eb0c38df3a629eaab020b43555f81ed5bcbfe55fc05ec8e0afc651547dff8f1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:14.787175Z","signature_b64":"/w4n72xRAtDrvOy+9mdBH/Tk98eyEsHm7WmcDzckjdeL1WMbx41gpcYUCLV7FS8qZ5mt9hdnbiRTg0uqr/UaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8d41e08011663c86f02d7fabf6ab77af65bab70bbf4c86aeffdf87b9673d385","last_reissued_at":"2026-05-18T01:10:14.786681Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:14.786681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear Convergence of Proximal Gradient Algorithm with Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.OC","authors_text":"Bo Wen, Ting Kei Pong, Xiaojun Chen","submitted_at":"2015-12-31T14:57:03Z","abstract_excerpt":"In this paper, we study the proximal gradient algorithm with extrapolation for minimizing the sum of a Lipschitz differentiable function and a proper closed convex function. Under the error bound condition used in [19] for analyzing the convergence of the proximal gradient algorithm, we show that there exists a threshold such that if the extrapolation coefficients are chosen below this threshold, then the sequence generated converges $R$-linearly to a stationary point of the problem. Moreover, the corresponding sequence of objective values is also $R$-linearly convergent. In addition, the thre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09302","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":""},"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":"1512.09302","created_at":"2026-05-18T01:10:14.786756+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.09302v2","created_at":"2026-05-18T01:10:14.786756+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09302","created_at":"2026-05-18T01:10:14.786756+00:00"},{"alias_kind":"pith_short_12","alias_value":"VDKB4CABCZR4","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"VDKB4CABCZR4Q3YC","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"VDKB4CAB","created_at":"2026-05-18T12:29:44.643036+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/VDKB4CABCZR4Q3YC275L62VXPL","json":"https://pith.science/pith/VDKB4CABCZR4Q3YC275L62VXPL.json","graph_json":"https://pith.science/api/pith-number/VDKB4CABCZR4Q3YC275L62VXPL/graph.json","events_json":"https://pith.science/api/pith-number/VDKB4CABCZR4Q3YC275L62VXPL/events.json","paper":"https://pith.science/paper/VDKB4CAB"},"agent_actions":{"view_html":"https://pith.science/pith/VDKB4CABCZR4Q3YC275L62VXPL","download_json":"https://pith.science/pith/VDKB4CABCZR4Q3YC275L62VXPL.json","view_paper":"https://pith.science/paper/VDKB4CAB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.09302&json=true","fetch_graph":"https://pith.science/api/pith-number/VDKB4CABCZR4Q3YC275L62VXPL/graph.json","fetch_events":"https://pith.science/api/pith-number/VDKB4CABCZR4Q3YC275L62VXPL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VDKB4CABCZR4Q3YC275L62VXPL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VDKB4CABCZR4Q3YC275L62VXPL/action/storage_attestation","attest_author":"https://pith.science/pith/VDKB4CABCZR4Q3YC275L62VXPL/action/author_attestation","sign_citation":"https://pith.science/pith/VDKB4CABCZR4Q3YC275L62VXPL/action/citation_signature","submit_replication":"https://pith.science/pith/VDKB4CABCZR4Q3YC275L62VXPL/action/replication_record"}},"created_at":"2026-05-18T01:10:14.786756+00:00","updated_at":"2026-05-18T01:10:14.786756+00:00"}