{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:J4EREFFSXOGIRFILOJF65U5P2P","short_pith_number":"pith:J4EREFFS","schema_version":"1.0","canonical_sha256":"4f091214b2bb8c88950b724beed3afd3f15a0fa9d9c94a236f85f3b094aa0264","source":{"kind":"arxiv","id":"0709.3186","version":3},"attestation_state":"computed","paper":{"title":"A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints","license":"","headline":"","cross_cats":["math.NA"],"primary_cat":"math.OC","authors_text":"Dirk A. Lorenz, Roland Griesse","submitted_at":"2007-09-20T10:59:42Z","abstract_excerpt":"Minimization problems in $\\ell^2$ for Tikhonov functionals with sparsity constraints are considered. Sparsity of the solution is ensured by a weighted $\\ell^1$ penalty term. The necessary and sufficient condition for optimality is shown to be slantly differentiable (Newton differentiable), hence a semismooth Newton method is applicable. Local superlinear convergence of this method is proved. Numerical examples are provided which show that our method compares favorably with existing approaches."},"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":"0709.3186","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.OC","submitted_at":"2007-09-20T10:59:42Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"e9dd020edc75ba96f0a5d907cd0825f4feb79b4db3a1079cdffeef0daee70b5f","abstract_canon_sha256":"27cb9883571a1d1ceea9f111551cb9eeb899d094bc7a01a62fac26ecb29f1abb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:51.067699Z","signature_b64":"Hrd8vfy1dc5LW/haFhkzQ5giP/02AymXqHNsgsMwic8fKPguTZzUKuZrPbTgKzoD7hEcElw412x3u1ZaiZJECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f091214b2bb8c88950b724beed3afd3f15a0fa9d9c94a236f85f3b094aa0264","last_reissued_at":"2026-05-18T04:38:51.067252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:51.067252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Semismooth Newton Method for Tikhonov Functionals with Sparsity Constraints","license":"","headline":"","cross_cats":["math.NA"],"primary_cat":"math.OC","authors_text":"Dirk A. Lorenz, Roland Griesse","submitted_at":"2007-09-20T10:59:42Z","abstract_excerpt":"Minimization problems in $\\ell^2$ for Tikhonov functionals with sparsity constraints are considered. Sparsity of the solution is ensured by a weighted $\\ell^1$ penalty term. The necessary and sufficient condition for optimality is shown to be slantly differentiable (Newton differentiable), hence a semismooth Newton method is applicable. Local superlinear convergence of this method is proved. Numerical examples are provided which show that our method compares favorably with existing approaches."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.3186","kind":"arxiv","version":3},"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":"0709.3186","created_at":"2026-05-18T04:38:51.067324+00:00"},{"alias_kind":"arxiv_version","alias_value":"0709.3186v3","created_at":"2026-05-18T04:38:51.067324+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.3186","created_at":"2026-05-18T04:38:51.067324+00:00"},{"alias_kind":"pith_short_12","alias_value":"J4EREFFSXOGI","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"J4EREFFSXOGIRFIL","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"J4EREFFS","created_at":"2026-05-18T12:25:55.427421+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/J4EREFFSXOGIRFILOJF65U5P2P","json":"https://pith.science/pith/J4EREFFSXOGIRFILOJF65U5P2P.json","graph_json":"https://pith.science/api/pith-number/J4EREFFSXOGIRFILOJF65U5P2P/graph.json","events_json":"https://pith.science/api/pith-number/J4EREFFSXOGIRFILOJF65U5P2P/events.json","paper":"https://pith.science/paper/J4EREFFS"},"agent_actions":{"view_html":"https://pith.science/pith/J4EREFFSXOGIRFILOJF65U5P2P","download_json":"https://pith.science/pith/J4EREFFSXOGIRFILOJF65U5P2P.json","view_paper":"https://pith.science/paper/J4EREFFS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0709.3186&json=true","fetch_graph":"https://pith.science/api/pith-number/J4EREFFSXOGIRFILOJF65U5P2P/graph.json","fetch_events":"https://pith.science/api/pith-number/J4EREFFSXOGIRFILOJF65U5P2P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J4EREFFSXOGIRFILOJF65U5P2P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J4EREFFSXOGIRFILOJF65U5P2P/action/storage_attestation","attest_author":"https://pith.science/pith/J4EREFFSXOGIRFILOJF65U5P2P/action/author_attestation","sign_citation":"https://pith.science/pith/J4EREFFSXOGIRFILOJF65U5P2P/action/citation_signature","submit_replication":"https://pith.science/pith/J4EREFFSXOGIRFILOJF65U5P2P/action/replication_record"}},"created_at":"2026-05-18T04:38:51.067324+00:00","updated_at":"2026-05-18T04:38:51.067324+00:00"}