{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6ON7TOP645STIQ3C7D2AKJ7L7U","short_pith_number":"pith:6ON7TOP6","canonical_record":{"source":{"id":"1212.5452","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-21T14:19:44Z","cross_cats_sorted":[],"title_canon_sha256":"0aa3c70ec4f38c288e79d422d1736bea81b764d9a985f82251516cf479f5b72d","abstract_canon_sha256":"be2d043da4e4515891f3caddc93c771e5c0b023e670fa387120da8b2e3c625d2"},"schema_version":"1.0"},"canonical_sha256":"f39bf9b9fee765344362f8f40527ebfd161c740faba3d431f1d590ff7180bbfe","source":{"kind":"arxiv","id":"1212.5452","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5452","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5452v1","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5452","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"pith_short_12","alias_value":"6ON7TOP645ST","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6ON7TOP645STIQ3C","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6ON7TOP6","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6ON7TOP645STIQ3C7D2AKJ7L7U","target":"record","payload":{"canonical_record":{"source":{"id":"1212.5452","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-21T14:19:44Z","cross_cats_sorted":[],"title_canon_sha256":"0aa3c70ec4f38c288e79d422d1736bea81b764d9a985f82251516cf479f5b72d","abstract_canon_sha256":"be2d043da4e4515891f3caddc93c771e5c0b023e670fa387120da8b2e3c625d2"},"schema_version":"1.0"},"canonical_sha256":"f39bf9b9fee765344362f8f40527ebfd161c740faba3d431f1d590ff7180bbfe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:49.557031Z","signature_b64":"WwelOJpc/adsKv5RfIwskOitkB/cF4D02OEYTI/RZazubymDpROUY/BjleSu0gp03VuxiWMPU733IP9/GsxxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f39bf9b9fee765344362f8f40527ebfd161c740faba3d431f1d590ff7180bbfe","last_reissued_at":"2026-05-18T01:30:49.556643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:49.556643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.5452","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bVW+mACLkF7D7N8dDyJq6V4M8wbDCBE8SQpGY1+hTpxc473U0sFcUBjVlHLgJJ/6/8lFADsGvm+Rg2G6yBIyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T16:58:22.358496Z"},"content_sha256":"3be9233c7f4a49a3a94d3f3e3b5f2b0971cacee84dafb69b0807d0253463a727","schema_version":"1.0","event_id":"sha256:3be9233c7f4a49a3a94d3f3e3b5f2b0971cacee84dafb69b0807d0253463a727"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6ON7TOP645STIQ3C7D2AKJ7L7U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Globally and Quadratically Convergent Algorithm with Efficient Implementation for Unconstrained Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Yaguang Yang","submitted_at":"2012-12-21T14:19:44Z","abstract_excerpt":"In this paper, an efficient modified Newton type algorithm is proposed for nonlinear unconstrianed optimization problems. The modified Hessian is a convex combination of the identity matrix (for steepest descent algorithm) and the Hessian matrix (for Newton algorithm). The coefficients of the convex combination are dynamically chosen in every iteration. The algorithm is proved to be globally and quadratically convergent for (convex and nonconvex) nonlinear functions. Efficient implementation is described. Numerical test on widely used CUTE test problems is conducted for the new algorithm. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5452","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LuVDqXw40R+9QGNjtSyCJlYMPVBpiaGf9FZEXOfs7SmAiS3uC9JSRHh476xVnq7AXtzIiR3/dv5K8AhXDhpXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T16:58:22.358961Z"},"content_sha256":"5b61444acbd53a4d8be83342154b7ce12501cde00dde9751aad5ee05244a9ca3","schema_version":"1.0","event_id":"sha256:5b61444acbd53a4d8be83342154b7ce12501cde00dde9751aad5ee05244a9ca3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ON7TOP645STIQ3C7D2AKJ7L7U/bundle.json","state_url":"https://pith.science/pith/6ON7TOP645STIQ3C7D2AKJ7L7U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ON7TOP645STIQ3C7D2AKJ7L7U/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T16:58:22Z","links":{"resolver":"https://pith.science/pith/6ON7TOP645STIQ3C7D2AKJ7L7U","bundle":"https://pith.science/pith/6ON7TOP645STIQ3C7D2AKJ7L7U/bundle.json","state":"https://pith.science/pith/6ON7TOP645STIQ3C7D2AKJ7L7U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ON7TOP645STIQ3C7D2AKJ7L7U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6ON7TOP645STIQ3C7D2AKJ7L7U","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":"be2d043da4e4515891f3caddc93c771e5c0b023e670fa387120da8b2e3c625d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-21T14:19:44Z","title_canon_sha256":"0aa3c70ec4f38c288e79d422d1736bea81b764d9a985f82251516cf479f5b72d"},"schema_version":"1.0","source":{"id":"1212.5452","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5452","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5452v1","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5452","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"pith_short_12","alias_value":"6ON7TOP645ST","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6ON7TOP645STIQ3C","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6ON7TOP6","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:5b61444acbd53a4d8be83342154b7ce12501cde00dde9751aad5ee05244a9ca3","target":"graph","created_at":"2026-05-18T01:30:49Z","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, an efficient modified Newton type algorithm is proposed for nonlinear unconstrianed optimization problems. The modified Hessian is a convex combination of the identity matrix (for steepest descent algorithm) and the Hessian matrix (for Newton algorithm). The coefficients of the convex combination are dynamically chosen in every iteration. The algorithm is proved to be globally and quadratically convergent for (convex and nonconvex) nonlinear functions. Efficient implementation is described. Numerical test on widely used CUTE test problems is conducted for the new algorithm. The ","authors_text":"Yaguang Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-21T14:19:44Z","title":"A Globally and Quadratically Convergent Algorithm with Efficient Implementation for Unconstrained Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5452","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":"sha256:3be9233c7f4a49a3a94d3f3e3b5f2b0971cacee84dafb69b0807d0253463a727","target":"record","created_at":"2026-05-18T01:30:49Z","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":"be2d043da4e4515891f3caddc93c771e5c0b023e670fa387120da8b2e3c625d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-21T14:19:44Z","title_canon_sha256":"0aa3c70ec4f38c288e79d422d1736bea81b764d9a985f82251516cf479f5b72d"},"schema_version":"1.0","source":{"id":"1212.5452","kind":"arxiv","version":1}},"canonical_sha256":"f39bf9b9fee765344362f8f40527ebfd161c740faba3d431f1d590ff7180bbfe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f39bf9b9fee765344362f8f40527ebfd161c740faba3d431f1d590ff7180bbfe","first_computed_at":"2026-05-18T01:30:49.556643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:49.556643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WwelOJpc/adsKv5RfIwskOitkB/cF4D02OEYTI/RZazubymDpROUY/BjleSu0gp03VuxiWMPU733IP9/GsxxBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:49.557031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5452","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3be9233c7f4a49a3a94d3f3e3b5f2b0971cacee84dafb69b0807d0253463a727","sha256:5b61444acbd53a4d8be83342154b7ce12501cde00dde9751aad5ee05244a9ca3"],"state_sha256":"316220a5759e2425b5989378c87a21f226833d5c42de994aebe4c74c39a71443"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p7l1bn/n2c6ND/0Uj/ZIgi+fUbH/ZeJt2Y4ojNG5/UaqDvSHRF83xioBoA/ARI68vIpGwp4Z3GnUrQ8qT8mWAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T16:58:22.361809Z","bundle_sha256":"8f6445add4dce816bd1f105e21b3da9d03f084d9e8192c5cb0124d860b9fb034"}}