{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:5JQBV4AAIJ7MX7UCDGVIPKBZWY","short_pith_number":"pith:5JQBV4AA","schema_version":"1.0","canonical_sha256":"ea601af000427ecbfe8219aa87a839b6350b7b9dfb1b9175463f9493628997be","source":{"kind":"arxiv","id":"2509.05765","version":1},"attestation_state":"computed","paper":{"title":"A Globalized Semismooth Newton Method for Prox-regular Optimization Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Pengcheng Wu, Shaohua Pan, Xiaoqi Yang, Yaohua Hu, Yuqia Wu","submitted_at":"2025-09-06T16:32:26Z","abstract_excerpt":"We are concerned with a class of nonconvex and nonsmooth composite optimization problems, comprising a twice differentiable function and a prox-regular function. We establish a sufficient condition for the proximal mapping of a prox-regular function to be single-valued and locally Lipschitz continuous. By virtue of this property, we propose a hybrid of proximal gradient and semismooth Newton methods for solving these composite optimization problems, which is a globalized semismooth Newton method. The whole sequence is shown to converge to an $L$-stationary point under a Kurdyka-{\\L}ojasiewicz "},"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":"2509.05765","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-09-06T16:32:26Z","cross_cats_sorted":[],"title_canon_sha256":"abf9bfe5afe5068d2a99e430b387a0f19924077d5351e72036622b2ec716ad6d","abstract_canon_sha256":"c2f2ca09cfcc6b43c50505f73f5d1275deb23415a6c568ce274e80cd2f4fc037"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:06:23.704645Z","signature_b64":"Pf/p8bEiF5+YrmQYZ0jcmiSVmj8hg0U5pnZfC5Va8nhF9ZJeBTkdEAuqwLYtrhRSpBq6x7tjxrm62hJOVn1mDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea601af000427ecbfe8219aa87a839b6350b7b9dfb1b9175463f9493628997be","last_reissued_at":"2026-07-05T12:06:23.704149Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:06:23.704149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Globalized Semismooth Newton Method for Prox-regular Optimization Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Pengcheng Wu, Shaohua Pan, Xiaoqi Yang, Yaohua Hu, Yuqia Wu","submitted_at":"2025-09-06T16:32:26Z","abstract_excerpt":"We are concerned with a class of nonconvex and nonsmooth composite optimization problems, comprising a twice differentiable function and a prox-regular function. We establish a sufficient condition for the proximal mapping of a prox-regular function to be single-valued and locally Lipschitz continuous. By virtue of this property, we propose a hybrid of proximal gradient and semismooth Newton methods for solving these composite optimization problems, which is a globalized semismooth Newton method. The whole sequence is shown to converge to an $L$-stationary point under a Kurdyka-{\\L}ojasiewicz "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05765","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/2509.05765/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":"2509.05765","created_at":"2026-07-05T12:06:23.704201+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.05765v1","created_at":"2026-07-05T12:06:23.704201+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.05765","created_at":"2026-07-05T12:06:23.704201+00:00"},{"alias_kind":"pith_short_12","alias_value":"5JQBV4AAIJ7M","created_at":"2026-07-05T12:06:23.704201+00:00"},{"alias_kind":"pith_short_16","alias_value":"5JQBV4AAIJ7MX7UC","created_at":"2026-07-05T12:06:23.704201+00:00"},{"alias_kind":"pith_short_8","alias_value":"5JQBV4AA","created_at":"2026-07-05T12:06:23.704201+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/5JQBV4AAIJ7MX7UCDGVIPKBZWY","json":"https://pith.science/pith/5JQBV4AAIJ7MX7UCDGVIPKBZWY.json","graph_json":"https://pith.science/api/pith-number/5JQBV4AAIJ7MX7UCDGVIPKBZWY/graph.json","events_json":"https://pith.science/api/pith-number/5JQBV4AAIJ7MX7UCDGVIPKBZWY/events.json","paper":"https://pith.science/paper/5JQBV4AA"},"agent_actions":{"view_html":"https://pith.science/pith/5JQBV4AAIJ7MX7UCDGVIPKBZWY","download_json":"https://pith.science/pith/5JQBV4AAIJ7MX7UCDGVIPKBZWY.json","view_paper":"https://pith.science/paper/5JQBV4AA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.05765&json=true","fetch_graph":"https://pith.science/api/pith-number/5JQBV4AAIJ7MX7UCDGVIPKBZWY/graph.json","fetch_events":"https://pith.science/api/pith-number/5JQBV4AAIJ7MX7UCDGVIPKBZWY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5JQBV4AAIJ7MX7UCDGVIPKBZWY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5JQBV4AAIJ7MX7UCDGVIPKBZWY/action/storage_attestation","attest_author":"https://pith.science/pith/5JQBV4AAIJ7MX7UCDGVIPKBZWY/action/author_attestation","sign_citation":"https://pith.science/pith/5JQBV4AAIJ7MX7UCDGVIPKBZWY/action/citation_signature","submit_replication":"https://pith.science/pith/5JQBV4AAIJ7MX7UCDGVIPKBZWY/action/replication_record"}},"created_at":"2026-07-05T12:06:23.704201+00:00","updated_at":"2026-07-05T12:06:23.704201+00:00"}