{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ONEX3DFBMKEDOEAMLHS5UOK6MI","short_pith_number":"pith:ONEX3DFB","schema_version":"1.0","canonical_sha256":"73497d8ca1628837100c59e5da395e621ce47a987efd4c6854903a94407ff1d0","source":{"kind":"arxiv","id":"1808.04648","version":1},"attestation_state":"computed","paper":{"title":"An Adaptive Primal-Dual Framework for Nonsmooth Convex Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ahmet Alacaoglu, Olivier Fercoq, Quoc Tran-Dinh, Volkan Cevher","submitted_at":"2018-08-14T12:00:35Z","abstract_excerpt":"We propose a new self-adaptive, double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov's smoothing technique via general Bregman distance functions. It self-adaptively selects the number of iterations in the inner loop to achieve a desired complexity bound without requiring the accuracy a priori as in variants of Augmented Lagrangian methods (ALM). We prove $\\BigO{\\frac{1}{k}}$-convergence rate on the last iterate of the outer sequence for both unconstrained and constrained settings in contrast to ergodic "},"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":"1808.04648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-14T12:00:35Z","cross_cats_sorted":[],"title_canon_sha256":"a4e69ab6130b5094da50c1e7d0c38e0c4f836465dc7929945b0c01ad8a57cc74","abstract_canon_sha256":"7797696d3a2702e5308365522e6e628681c84deadf005c9bb64ed3cb5db23efa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:11.960440Z","signature_b64":"G6AC5zQqkbgieHd3kx4SzLl8DlfUM7+D3VXRS5RiUWBsMASfRM2GltNzyHESUg51X1eJ/FI5Zeukk4AsRP9VAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73497d8ca1628837100c59e5da395e621ce47a987efd4c6854903a94407ff1d0","last_reissued_at":"2026-05-18T00:08:11.959799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:11.959799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Adaptive Primal-Dual Framework for Nonsmooth Convex Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ahmet Alacaoglu, Olivier Fercoq, Quoc Tran-Dinh, Volkan Cevher","submitted_at":"2018-08-14T12:00:35Z","abstract_excerpt":"We propose a new self-adaptive, double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov's smoothing technique via general Bregman distance functions. It self-adaptively selects the number of iterations in the inner loop to achieve a desired complexity bound without requiring the accuracy a priori as in variants of Augmented Lagrangian methods (ALM). We prove $\\BigO{\\frac{1}{k}}$-convergence rate on the last iterate of the outer sequence for both unconstrained and constrained settings in contrast to ergodic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04648","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":""},"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":"1808.04648","created_at":"2026-05-18T00:08:11.959882+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.04648v1","created_at":"2026-05-18T00:08:11.959882+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04648","created_at":"2026-05-18T00:08:11.959882+00:00"},{"alias_kind":"pith_short_12","alias_value":"ONEX3DFBMKED","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"ONEX3DFBMKEDOEAM","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"ONEX3DFB","created_at":"2026-05-18T12:32:43.782077+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/ONEX3DFBMKEDOEAMLHS5UOK6MI","json":"https://pith.science/pith/ONEX3DFBMKEDOEAMLHS5UOK6MI.json","graph_json":"https://pith.science/api/pith-number/ONEX3DFBMKEDOEAMLHS5UOK6MI/graph.json","events_json":"https://pith.science/api/pith-number/ONEX3DFBMKEDOEAMLHS5UOK6MI/events.json","paper":"https://pith.science/paper/ONEX3DFB"},"agent_actions":{"view_html":"https://pith.science/pith/ONEX3DFBMKEDOEAMLHS5UOK6MI","download_json":"https://pith.science/pith/ONEX3DFBMKEDOEAMLHS5UOK6MI.json","view_paper":"https://pith.science/paper/ONEX3DFB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.04648&json=true","fetch_graph":"https://pith.science/api/pith-number/ONEX3DFBMKEDOEAMLHS5UOK6MI/graph.json","fetch_events":"https://pith.science/api/pith-number/ONEX3DFBMKEDOEAMLHS5UOK6MI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ONEX3DFBMKEDOEAMLHS5UOK6MI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ONEX3DFBMKEDOEAMLHS5UOK6MI/action/storage_attestation","attest_author":"https://pith.science/pith/ONEX3DFBMKEDOEAMLHS5UOK6MI/action/author_attestation","sign_citation":"https://pith.science/pith/ONEX3DFBMKEDOEAMLHS5UOK6MI/action/citation_signature","submit_replication":"https://pith.science/pith/ONEX3DFBMKEDOEAMLHS5UOK6MI/action/replication_record"}},"created_at":"2026-05-18T00:08:11.959882+00:00","updated_at":"2026-05-18T00:08:11.959882+00:00"}