{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4RGQZZN7SXLMVDB4HPDLGYWE72","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":"e7d9846022e9c0fd631bb731e887049043b0e49da1f2ed4be505b5ef768cb3fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-29T16:00:13Z","title_canon_sha256":"7228c4fc3701a20d7330414226bb0faed650939ee477271c9104d86649ba93e8"},"schema_version":"1.0","source":{"id":"1601.08166","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.08166","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"arxiv_version","alias_value":"1601.08166v1","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.08166","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"pith_short_12","alias_value":"4RGQZZN7SXLM","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4RGQZZN7SXLMVDB4","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4RGQZZN7","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:fd92b5dbe88b3bf8645a4f6ef1bd7ea1c5f161396ac6a4c335a7a6c232998688","target":"graph","created_at":"2026-05-18T01:21:40Z","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":"In this paper we propose two proximal gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either concave or convex. In the iterative schemes, we perform a proximal step with respect to the nonsmooth numerator and a gradient step with respect to the smooth denominator. The algorithm in case of a concave denominator has the particularity that it generates sequences which approach both the (global) optimal solutions set and the optimal objective value of ","authors_text":"Ern\\\"o Robert Csetnek, Radu Ioan Bot","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-29T16:00:13Z","title":"Proximal-gradient algorithms for fractional programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08166","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:cd14ffa151d10e683895a555a651dcdd1978a1868cf809091d832f12fbf9f67a","target":"record","created_at":"2026-05-18T01:21:40Z","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":"e7d9846022e9c0fd631bb731e887049043b0e49da1f2ed4be505b5ef768cb3fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-01-29T16:00:13Z","title_canon_sha256":"7228c4fc3701a20d7330414226bb0faed650939ee477271c9104d86649ba93e8"},"schema_version":"1.0","source":{"id":"1601.08166","kind":"arxiv","version":1}},"canonical_sha256":"e44d0ce5bf95d6ca8c3c3bc6b362c4fea63d6e12f6d7626fa53d0451106ed916","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e44d0ce5bf95d6ca8c3c3bc6b362c4fea63d6e12f6d7626fa53d0451106ed916","first_computed_at":"2026-05-18T01:21:40.198623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:40.198623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wPpb6VMQ9XmmAR/WGnYsMon4x0CeVG5OybvYisP0Ei5lo7XnF9ajQ2R/AwDHprGgZfBbrp6WHNQEBh766fTyBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:40.199108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.08166","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd14ffa151d10e683895a555a651dcdd1978a1868cf809091d832f12fbf9f67a","sha256:fd92b5dbe88b3bf8645a4f6ef1bd7ea1c5f161396ac6a4c335a7a6c232998688"],"state_sha256":"bc83a83b0d78644a445160bbfbb93acc2a5f5229d2d5687548d1567dbbc40ccb"}