{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LC6JDMOEXJLAQ27BGZR5MFVNGJ","short_pith_number":"pith:LC6JDMOE","schema_version":"1.0","canonical_sha256":"58bc91b1c4ba56086be13663d616ad325f1df79e0911b9575db463c9ab351e23","source":{"kind":"arxiv","id":"1605.09750","version":4},"attestation_state":"computed","paper":{"title":"Nonconvex penalization of switching control of partial differential equations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Armin Rund, Christian Clason, Karl Kunisch","submitted_at":"2016-05-31T18:12:07Z","abstract_excerpt":"This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control. A standard approach to treat constraints in nonlinear optimization is penalization, in particular using $L^1$-type norms. Applying this approach to the switching constraint leads to a nonsmooth and nonconvex infinite-dimensional minimization problem which is challenging both analytically and numerically. Adding $H^1$ regularization or restricting to a finite-dimensional control space allows showing existence of optimal controls. First-o"},"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":"1605.09750","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2016-05-31T18:12:07Z","cross_cats_sorted":[],"title_canon_sha256":"09844f92fa944b853963f9b67dcdbc1faa1fc00953379fe225d32d0982bf9286","abstract_canon_sha256":"be6ca0d2c01d4835603840cfc74d0e39a072abfddd88be5ed28aea47aceb0d19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:24.557235Z","signature_b64":"yuPIdrBKg2pZEfhOydRUociFpMSG4HZyMKNGe5zaCk9m/BRNC4YAC07C9NBho+R4f3tw133hCobJ/scJtmdjBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58bc91b1c4ba56086be13663d616ad325f1df79e0911b9575db463c9ab351e23","last_reissued_at":"2026-05-18T00:17:24.556475Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:24.556475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonconvex penalization of switching control of partial differential equations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Armin Rund, Christian Clason, Karl Kunisch","submitted_at":"2016-05-31T18:12:07Z","abstract_excerpt":"This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control. A standard approach to treat constraints in nonlinear optimization is penalization, in particular using $L^1$-type norms. Applying this approach to the switching constraint leads to a nonsmooth and nonconvex infinite-dimensional minimization problem which is challenging both analytically and numerically. Adding $H^1$ regularization or restricting to a finite-dimensional control space allows showing existence of optimal controls. First-o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09750","kind":"arxiv","version":4},"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":"1605.09750","created_at":"2026-05-18T00:17:24.556611+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.09750v4","created_at":"2026-05-18T00:17:24.556611+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09750","created_at":"2026-05-18T00:17:24.556611+00:00"},{"alias_kind":"pith_short_12","alias_value":"LC6JDMOEXJLA","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LC6JDMOEXJLAQ27B","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LC6JDMOE","created_at":"2026-05-18T12:30:29.479603+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/LC6JDMOEXJLAQ27BGZR5MFVNGJ","json":"https://pith.science/pith/LC6JDMOEXJLAQ27BGZR5MFVNGJ.json","graph_json":"https://pith.science/api/pith-number/LC6JDMOEXJLAQ27BGZR5MFVNGJ/graph.json","events_json":"https://pith.science/api/pith-number/LC6JDMOEXJLAQ27BGZR5MFVNGJ/events.json","paper":"https://pith.science/paper/LC6JDMOE"},"agent_actions":{"view_html":"https://pith.science/pith/LC6JDMOEXJLAQ27BGZR5MFVNGJ","download_json":"https://pith.science/pith/LC6JDMOEXJLAQ27BGZR5MFVNGJ.json","view_paper":"https://pith.science/paper/LC6JDMOE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.09750&json=true","fetch_graph":"https://pith.science/api/pith-number/LC6JDMOEXJLAQ27BGZR5MFVNGJ/graph.json","fetch_events":"https://pith.science/api/pith-number/LC6JDMOEXJLAQ27BGZR5MFVNGJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LC6JDMOEXJLAQ27BGZR5MFVNGJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LC6JDMOEXJLAQ27BGZR5MFVNGJ/action/storage_attestation","attest_author":"https://pith.science/pith/LC6JDMOEXJLAQ27BGZR5MFVNGJ/action/author_attestation","sign_citation":"https://pith.science/pith/LC6JDMOEXJLAQ27BGZR5MFVNGJ/action/citation_signature","submit_replication":"https://pith.science/pith/LC6JDMOEXJLAQ27BGZR5MFVNGJ/action/replication_record"}},"created_at":"2026-05-18T00:17:24.556611+00:00","updated_at":"2026-05-18T00:17:24.556611+00:00"}