{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3WNCJKTPISIGTNFM2WKQBABUNT","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":"159549b056821344581783125e80a3e892942944910ee0a4456c9ebc9e73a99a","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-11-16T14:28:15Z","title_canon_sha256":"bcb1a88ec38a4feacca55a13da9eceb96f8847aa2b3b5138e113cb3046ad7991"},"schema_version":"1.0","source":{"id":"1711.06570","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06570","created_at":"2026-05-18T00:30:18Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06570v1","created_at":"2026-05-18T00:30:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06570","created_at":"2026-05-18T00:30:18Z"},{"alias_kind":"pith_short_12","alias_value":"3WNCJKTPISIG","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3WNCJKTPISIGTNFM","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3WNCJKTP","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:a203dbd98b4960af58709ac47f7f6d7538a7e8d0d54edd0c47044cbd835b2029","target":"graph","created_at":"2026-05-18T00:30:18Z","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"},"paper":{"abstract_excerpt":"We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system of proximal-gradient type stated in connection with the minimization of the sum of a nonsmooth convex and a (possibly nonconvex) smooth function. The convergence of the generated trajectory to a critical point of the objective is ensured provided a regularization of the objective function satisfies the Kurdyka-\\L{}ojasiewicz property. We also provide convergence rates for the trajectory formulated in terms of the \\L{}ojasiewicz exponent.","authors_text":"Ern\\\"o Robert Csetnek, Radu Ioan Bot, Szil\\'ard Csaba L\\'aszl\\'o","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-11-16T14:28:15Z","title":"Approaching nonsmooth nonconvex minimization through second order proximal-gradient dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06570","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":"sha256:9a94ab2efa8646a091717423d39b60f4a28b42184aebd6ffd5041819a0cf1088","target":"record","created_at":"2026-05-18T00:30:18Z","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":"159549b056821344581783125e80a3e892942944910ee0a4456c9ebc9e73a99a","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-11-16T14:28:15Z","title_canon_sha256":"bcb1a88ec38a4feacca55a13da9eceb96f8847aa2b3b5138e113cb3046ad7991"},"schema_version":"1.0","source":{"id":"1711.06570","kind":"arxiv","version":1}},"canonical_sha256":"dd9a24aa6f449069b4acd5950080346cd396221e6a0bbd6688cd197e1dee721d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd9a24aa6f449069b4acd5950080346cd396221e6a0bbd6688cd197e1dee721d","first_computed_at":"2026-05-18T00:30:18.508184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:18.508184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UeAlHiz8eYTx1TNNHGzf1KpKciN21RffVtKBoEXckJLC53M6dsZuHEzGfoEEgrkJLOzcvmcseZ3ZWNJhL0R/Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:18.508869Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.06570","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a94ab2efa8646a091717423d39b60f4a28b42184aebd6ffd5041819a0cf1088","sha256:a203dbd98b4960af58709ac47f7f6d7538a7e8d0d54edd0c47044cbd835b2029"],"state_sha256":"bedb52490ba91b4209c488e91ed7610cd68e6f5e756ea3d0532ed7f6ff3c91ec"}