{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:R5MZR2NZMJQZCW6RXGSLCJO3YI","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":"2e8716c91e014d268e6d58068f16a76eb9177029a5b60da09231fb0ec62319fb","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-17T17:05:15Z","title_canon_sha256":"dde7b1316ece5d5fbf13d617ec144d1d901d35533fe81be64097c8dba5ce598b"},"schema_version":"1.0","source":{"id":"1812.06896","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.06896","created_at":"2026-06-04T20:13:48Z"},{"alias_kind":"arxiv_version","alias_value":"1812.06896v4","created_at":"2026-06-04T20:13:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.06896","created_at":"2026-06-04T20:13:48Z"},{"alias_kind":"pith_short_12","alias_value":"R5MZR2NZMJQZ","created_at":"2026-06-04T20:13:48Z"},{"alias_kind":"pith_short_16","alias_value":"R5MZR2NZMJQZCW6R","created_at":"2026-06-04T20:13:48Z"},{"alias_kind":"pith_short_8","alias_value":"R5MZR2NZ","created_at":"2026-06-04T20:13:48Z"}],"graph_snapshots":[{"event_id":"sha256:63d98312ad64009486422b6cdef88e83da4edcd280b5949d33b1e9c7f02786df","target":"graph","created_at":"2026-06-04T20:13:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1812.06896/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A merger of two optimization frameworks is introduced: SEquential Subspace OPtimization (SESOP) with MultiGrid (MG) optimization. At each iteration of the algorithm, the search direction implied by the coarse-grid correction process of MG is added to the low dimensional search-space of SESOP, which includes the preconditioned gradient and search directions involving the previous iterates, called {\\em history}. Numerical experiments demonstrate the effectiveness of this approach. We then study the asymptotic convergence factor of the two-level version of SESOP-MG (dubbed SESOP-TG) for optimizat","authors_text":"Irad Yavneh, Michael Zibulevsky, Tao Hong","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-17T17:05:15Z","title":"Merging Multigrid Optimization with SESOP"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.06896","kind":"arxiv","version":4},"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":"sha256:72a0c0bede3f58a7f02446d389b187123b3d7503bd9a3e7efd16ec2f51c778fc","target":"record","created_at":"2026-06-04T20:13:48Z","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":"2e8716c91e014d268e6d58068f16a76eb9177029a5b60da09231fb0ec62319fb","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-17T17:05:15Z","title_canon_sha256":"dde7b1316ece5d5fbf13d617ec144d1d901d35533fe81be64097c8dba5ce598b"},"schema_version":"1.0","source":{"id":"1812.06896","kind":"arxiv","version":4}},"canonical_sha256":"8f5998e9b96261915bd1b9a4b125dbc2344b9713856de59b030855590786010c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f5998e9b96261915bd1b9a4b125dbc2344b9713856de59b030855590786010c","first_computed_at":"2026-06-04T20:13:48.658062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T20:13:48.658062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WAlLl0LzmQ6uu5p0jxbEPZyrhPAvE582ZMBRZaG+LJkqnz2SYZotTTR1OciEbpH3rgeQPJr31efhKTv1AbcrBQ==","signature_status":"signed_v1","signed_at":"2026-06-04T20:13:48.658744Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.06896","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72a0c0bede3f58a7f02446d389b187123b3d7503bd9a3e7efd16ec2f51c778fc","sha256:63d98312ad64009486422b6cdef88e83da4edcd280b5949d33b1e9c7f02786df"],"state_sha256":"ec5099efedb41b3192d0cb42baf19bffc969c4df526df6f16ae7d9dcc7570d33"}