{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:TBJ73W2ZQWLDPN2BXRMV6BKBVK","short_pith_number":"pith:TBJ73W2Z","schema_version":"1.0","canonical_sha256":"9853fddb59859637b741bc595f0541aa8c0421394133975df32de07821c299a2","source":{"kind":"arxiv","id":"2410.19506","version":1},"attestation_state":"computed","paper":{"title":"Optimization with First Order Algorithms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Charles Dossal, Nicolas Papadakis, Samuel Hurault","submitted_at":"2024-10-25T12:19:31Z","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"},"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":"2410.19506","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-25T12:19:31Z","cross_cats_sorted":[],"title_canon_sha256":"81a3eaece827b42c9e9f54d62296cf25ae5815328bd904de07e7e1d6eb384216","abstract_canon_sha256":"8c98523bf97618b47ed6ab82d240d019120c42d33a700c6d5d616683b25bbef5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:25:57.573556Z","signature_b64":"2+15kbVRfVeTAE+xaaVCR+Ou47vGOzXtxGS651DX+K1mL/GJUu1nISOzDnVTvHIlp6knEqaJRvmcmc07JUr1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9853fddb59859637b741bc595f0541aa8c0421394133975df32de07821c299a2","last_reissued_at":"2026-07-05T09:25:57.573159Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:25:57.573159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimization with First Order Algorithms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Charles Dossal, Nicolas Papadakis, Samuel Hurault","submitted_at":"2024-10-25T12:19:31Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.19506","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.19506/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":"2410.19506","created_at":"2026-07-05T09:25:57.573223+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.19506v1","created_at":"2026-07-05T09:25:57.573223+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.19506","created_at":"2026-07-05T09:25:57.573223+00:00"},{"alias_kind":"pith_short_12","alias_value":"TBJ73W2ZQWLD","created_at":"2026-07-05T09:25:57.573223+00:00"},{"alias_kind":"pith_short_16","alias_value":"TBJ73W2ZQWLDPN2B","created_at":"2026-07-05T09:25:57.573223+00:00"},{"alias_kind":"pith_short_8","alias_value":"TBJ73W2Z","created_at":"2026-07-05T09:25:57.573223+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.26318","citing_title":"Sparse symmetric generalized inverses for sparse symmetric matrices","ref_index":16,"is_internal_anchor":false},{"citing_arxiv_id":"2605.20962","citing_title":"No-regret optimization of time-varying bilevel problems","ref_index":165,"is_internal_anchor":false},{"citing_arxiv_id":"2605.12085","citing_title":"A Line--Search--Based Stochastic Gradient Method for 3D Computed Tomography","ref_index":13,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TBJ73W2ZQWLDPN2BXRMV6BKBVK","json":"https://pith.science/pith/TBJ73W2ZQWLDPN2BXRMV6BKBVK.json","graph_json":"https://pith.science/api/pith-number/TBJ73W2ZQWLDPN2BXRMV6BKBVK/graph.json","events_json":"https://pith.science/api/pith-number/TBJ73W2ZQWLDPN2BXRMV6BKBVK/events.json","paper":"https://pith.science/paper/TBJ73W2Z"},"agent_actions":{"view_html":"https://pith.science/pith/TBJ73W2ZQWLDPN2BXRMV6BKBVK","download_json":"https://pith.science/pith/TBJ73W2ZQWLDPN2BXRMV6BKBVK.json","view_paper":"https://pith.science/paper/TBJ73W2Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.19506&json=true","fetch_graph":"https://pith.science/api/pith-number/TBJ73W2ZQWLDPN2BXRMV6BKBVK/graph.json","fetch_events":"https://pith.science/api/pith-number/TBJ73W2ZQWLDPN2BXRMV6BKBVK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TBJ73W2ZQWLDPN2BXRMV6BKBVK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TBJ73W2ZQWLDPN2BXRMV6BKBVK/action/storage_attestation","attest_author":"https://pith.science/pith/TBJ73W2ZQWLDPN2BXRMV6BKBVK/action/author_attestation","sign_citation":"https://pith.science/pith/TBJ73W2ZQWLDPN2BXRMV6BKBVK/action/citation_signature","submit_replication":"https://pith.science/pith/TBJ73W2ZQWLDPN2BXRMV6BKBVK/action/replication_record"}},"created_at":"2026-07-05T09:25:57.573223+00:00","updated_at":"2026-07-05T09:25:57.573223+00:00"}