{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TBJ73W2ZQWLDPN2BXRMV6BKBVK","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":"8c98523bf97618b47ed6ab82d240d019120c42d33a700c6d5d616683b25bbef5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-25T12:19:31Z","title_canon_sha256":"81a3eaece827b42c9e9f54d62296cf25ae5815328bd904de07e7e1d6eb384216"},"schema_version":"1.0","source":{"id":"2410.19506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.19506","created_at":"2026-07-05T09:25:57Z"},{"alias_kind":"arxiv_version","alias_value":"2410.19506v1","created_at":"2026-07-05T09:25:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.19506","created_at":"2026-07-05T09:25:57Z"},{"alias_kind":"pith_short_12","alias_value":"TBJ73W2ZQWLD","created_at":"2026-07-05T09:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"TBJ73W2ZQWLDPN2B","created_at":"2026-07-05T09:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"TBJ73W2Z","created_at":"2026-07-05T09:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:42374c8e9070d6a02a806c4b5b2ef7f16c8fb5502dd7fe7f64a6d4cb78de8db0","target":"graph","created_at":"2026-07-05T09:25:57Z","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/2410.19506/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze the most classical first-order optimization algorithms. We aim to provide readers with both a practical and theoretical understanding in how and why these algorithms converge to minimizers of convex functions. The main algorithms covered in these notes include gradient descent, Forward-Backward splitting, Douglas-Rachford splitting, the Alternating Direction M","authors_text":"Charles Dossal, Nicolas Papadakis, Samuel Hurault","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-25T12:19:31Z","title":"Optimization with First Order Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.19506","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":"sha256:6670ada136eeaff0410374b552e730798afe1031386b4335691c69eb7270e4b1","target":"record","created_at":"2026-07-05T09:25:57Z","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":"8c98523bf97618b47ed6ab82d240d019120c42d33a700c6d5d616683b25bbef5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-25T12:19:31Z","title_canon_sha256":"81a3eaece827b42c9e9f54d62296cf25ae5815328bd904de07e7e1d6eb384216"},"schema_version":"1.0","source":{"id":"2410.19506","kind":"arxiv","version":1}},"canonical_sha256":"9853fddb59859637b741bc595f0541aa8c0421394133975df32de07821c299a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9853fddb59859637b741bc595f0541aa8c0421394133975df32de07821c299a2","first_computed_at":"2026-07-05T09:25:57.573159Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:25:57.573159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2+15kbVRfVeTAE+xaaVCR+Ou47vGOzXtxGS651DX+K1mL/GJUu1nISOzDnVTvHIlp6knEqaJRvmcmc07JUr1Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:25:57.573556Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.19506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6670ada136eeaff0410374b552e730798afe1031386b4335691c69eb7270e4b1","sha256:42374c8e9070d6a02a806c4b5b2ef7f16c8fb5502dd7fe7f64a6d4cb78de8db0"],"state_sha256":"72f6119d197db2d252f672b29d5f59938a51504f822ec48b6471bc787ab7f2b4"}