{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:7HQ3CH2TL7OL34LNEXHWZV4PFK","short_pith_number":"pith:7HQ3CH2T","schema_version":"1.0","canonical_sha256":"f9e1b11f535fdcbdf16d25cf6cd78f2a832ee6ba628de5ee6c5e3463e2081579","source":{"kind":"arxiv","id":"1603.04460","version":1},"attestation_state":"computed","paper":{"title":"Levenberg-Marquardt dynamics associated to variational inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Ern\\\"o Robert Csetnek, Radu Ioan Bot","submitted_at":"2016-03-14T20:29:28Z","abstract_excerpt":"In connection with the optimization problem $$\\inf_{x\\in argmin \\Psi}\\{\\Phi(x)+\\Theta(x)\\},$$ where $\\Phi$ is a proper, convex and lower semicontinuous function and $\\Theta$ and $\\Psi$ are convex and smooth functions defined on a real Hilbert space, we investigate the asymptotic behavior of the trajectories of the nonautonomous Levenberg-Marquardt dynamical system \\begin{equation*}\\left\\{ \\begin{array}{ll} v(t)\\in\\partial\\Phi(x(t))\\\\ \\lambda(t)\\dot x(t) + \\dot v(t) + v(t) + \\nabla \\Theta(x(t))+\\beta(t)\\nabla \\Psi(x(t))=0, \\end{array}\\right.\\end{equation*} where $\\lambda$ and $\\beta$ are functi"},"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":"1603.04460","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-14T20:29:28Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"262bb447f54d5c7382d93cf2b5949ece1216f63fda14f90028781a40963e12b5","abstract_canon_sha256":"dd9f7eec8e00d85f48704ec7b8f42434f76d59fada10af8c816b4fc72da5b916"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:04.884550Z","signature_b64":"84G2RmNWN9iReN9coYicTcOnlaWJHLz11YevKDSVQlCQjbX2Y08nnxXgdfail6eCppFeJZ+kk6SQcutLYP6PDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9e1b11f535fdcbdf16d25cf6cd78f2a832ee6ba628de5ee6c5e3463e2081579","last_reissued_at":"2026-05-18T01:19:04.883899Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:04.883899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Levenberg-Marquardt dynamics associated to variational inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OC","authors_text":"Ern\\\"o Robert Csetnek, Radu Ioan Bot","submitted_at":"2016-03-14T20:29:28Z","abstract_excerpt":"In connection with the optimization problem $$\\inf_{x\\in argmin \\Psi}\\{\\Phi(x)+\\Theta(x)\\},$$ where $\\Phi$ is a proper, convex and lower semicontinuous function and $\\Theta$ and $\\Psi$ are convex and smooth functions defined on a real Hilbert space, we investigate the asymptotic behavior of the trajectories of the nonautonomous Levenberg-Marquardt dynamical system \\begin{equation*}\\left\\{ \\begin{array}{ll} v(t)\\in\\partial\\Phi(x(t))\\\\ \\lambda(t)\\dot x(t) + \\dot v(t) + v(t) + \\nabla \\Theta(x(t))+\\beta(t)\\nabla \\Psi(x(t))=0, \\end{array}\\right.\\end{equation*} where $\\lambda$ and $\\beta$ are functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04460","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":""},"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":"1603.04460","created_at":"2026-05-18T01:19:04.883988+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.04460v1","created_at":"2026-05-18T01:19:04.883988+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04460","created_at":"2026-05-18T01:19:04.883988+00:00"},{"alias_kind":"pith_short_12","alias_value":"7HQ3CH2TL7OL","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7HQ3CH2TL7OL34LN","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7HQ3CH2T","created_at":"2026-05-18T12:30:04.600751+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/7HQ3CH2TL7OL34LNEXHWZV4PFK","json":"https://pith.science/pith/7HQ3CH2TL7OL34LNEXHWZV4PFK.json","graph_json":"https://pith.science/api/pith-number/7HQ3CH2TL7OL34LNEXHWZV4PFK/graph.json","events_json":"https://pith.science/api/pith-number/7HQ3CH2TL7OL34LNEXHWZV4PFK/events.json","paper":"https://pith.science/paper/7HQ3CH2T"},"agent_actions":{"view_html":"https://pith.science/pith/7HQ3CH2TL7OL34LNEXHWZV4PFK","download_json":"https://pith.science/pith/7HQ3CH2TL7OL34LNEXHWZV4PFK.json","view_paper":"https://pith.science/paper/7HQ3CH2T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.04460&json=true","fetch_graph":"https://pith.science/api/pith-number/7HQ3CH2TL7OL34LNEXHWZV4PFK/graph.json","fetch_events":"https://pith.science/api/pith-number/7HQ3CH2TL7OL34LNEXHWZV4PFK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7HQ3CH2TL7OL34LNEXHWZV4PFK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7HQ3CH2TL7OL34LNEXHWZV4PFK/action/storage_attestation","attest_author":"https://pith.science/pith/7HQ3CH2TL7OL34LNEXHWZV4PFK/action/author_attestation","sign_citation":"https://pith.science/pith/7HQ3CH2TL7OL34LNEXHWZV4PFK/action/citation_signature","submit_replication":"https://pith.science/pith/7HQ3CH2TL7OL34LNEXHWZV4PFK/action/replication_record"}},"created_at":"2026-05-18T01:19:04.883988+00:00","updated_at":"2026-05-18T01:19:04.883988+00:00"}