{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ONRH7IKROEK3JJW554R3UJWQV6","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":"03599e1035062c0fd0f8a03e48504b5c02a1a3501eea5bae05ad5ca30b9902b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-18T05:14:02Z","title_canon_sha256":"6d5d8ef7b4f38bcaab0ed9c9545616280f9a3d5d387096f8ed8592cddde24f06"},"schema_version":"1.0","source":{"id":"1508.04214","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04214","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04214v3","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04214","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"pith_short_12","alias_value":"ONRH7IKROEK3","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"ONRH7IKROEK3JJW5","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"ONRH7IKR","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:f3a832ffffd30d986c0965d27f4fe45282d4c7ad852de07e0c3e5560677848a6","target":"graph","created_at":"2026-05-18T00:42:18Z","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 consider the minimization or maximization of the $J$th largest eigenvalue of an analytic and Hermitian matrix-valued function, and build on Mengi et al. (2014, SIAM J. Matrix Anal. Appl., 35, 699-724). This work addresses the setting when the matrix-valued function involved is very large. We describe subspace procedures that convert the original problem into a small-scale one by means of orthogonal projections and restrictions to certain subspaces, and that gradually expand these subspaces based on the optimal solutions of small-scale problems. Global convergence and superlinear rate-of-con","authors_text":"Emre Mengi, Fatih Kangal, Karl Meerbergen, Wim Michiels","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-18T05:14:02Z","title":"A Subspace Method for Large Scale Eigenvalue Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04214","kind":"arxiv","version":3},"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:f5f5831621dde1206a18999ff68ab85f9b3e9193a560704f604b3310edbbd1e8","target":"record","created_at":"2026-05-18T00:42:18Z","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":"03599e1035062c0fd0f8a03e48504b5c02a1a3501eea5bae05ad5ca30b9902b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-18T05:14:02Z","title_canon_sha256":"6d5d8ef7b4f38bcaab0ed9c9545616280f9a3d5d387096f8ed8592cddde24f06"},"schema_version":"1.0","source":{"id":"1508.04214","kind":"arxiv","version":3}},"canonical_sha256":"73627fa1517115b4a6ddef23ba26d0af93c55a1bd978a5e8ed5680ca4b494702","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73627fa1517115b4a6ddef23ba26d0af93c55a1bd978a5e8ed5680ca4b494702","first_computed_at":"2026-05-18T00:42:18.112102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:18.112102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zUMIulv4HAMR7BLQQ86RN5fEkTaT2AX53O9VhijtuTWllQN+EdQGiSZr6XOd5JpoxFudqCEZ0iOJ8R4LdQw+BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:18.112752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.04214","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5f5831621dde1206a18999ff68ab85f9b3e9193a560704f604b3310edbbd1e8","sha256:f3a832ffffd30d986c0965d27f4fe45282d4c7ad852de07e0c3e5560677848a6"],"state_sha256":"99251ace2a1ae2db690710068b20fd6a1e837dc2fcb1e5f80bfcaecaa2c8cee3"}