{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GA62SKAOAFBVAEKWZ7KOK62DE6","short_pith_number":"pith:GA62SKAO","canonical_record":{"source":{"id":"1406.0942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-06-04T05:12:13Z","cross_cats_sorted":[],"title_canon_sha256":"3b8ddb9ee15fdfbde6d803a0abf9f80f5ac74089c914cbc19510c4533a870499","abstract_canon_sha256":"4a2f179c5b8ad1b4ad0cb9783d15d83468a70461b326d9f70ef9a8f5d58cd37c"},"schema_version":"1.0"},"canonical_sha256":"303da9280e0143501156cfd4e57b4327ab028a1661106b475fd9a4a8ce7d9594","source":{"kind":"arxiv","id":"1406.0942","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0942","created_at":"2026-05-18T02:50:30Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0942v1","created_at":"2026-05-18T02:50:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0942","created_at":"2026-05-18T02:50:30Z"},{"alias_kind":"pith_short_12","alias_value":"GA62SKAOAFBV","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"GA62SKAOAFBVAEKW","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"GA62SKAO","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GA62SKAOAFBVAEKWZ7KOK62DE6","target":"record","payload":{"canonical_record":{"source":{"id":"1406.0942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-06-04T05:12:13Z","cross_cats_sorted":[],"title_canon_sha256":"3b8ddb9ee15fdfbde6d803a0abf9f80f5ac74089c914cbc19510c4533a870499","abstract_canon_sha256":"4a2f179c5b8ad1b4ad0cb9783d15d83468a70461b326d9f70ef9a8f5d58cd37c"},"schema_version":"1.0"},"canonical_sha256":"303da9280e0143501156cfd4e57b4327ab028a1661106b475fd9a4a8ce7d9594","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:30.692674Z","signature_b64":"Lme8Kg8n4Cyv8RJxSn/g82WqzDgZnHmkEyI/JlGopsd4mkycFFkIqXP0atukRUSwxpgj30ENiX9xFFLtPHjlAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"303da9280e0143501156cfd4e57b4327ab028a1661106b475fd9a4a8ce7d9594","last_reissued_at":"2026-05-18T02:50:30.692131Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:30.692131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.0942","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":"2026-05-18T02:50:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q6oidPbPRPXZESDxd3L+VBUkEAxCVz/qH9Rdjh+SJjn3Xddz9iV+9jbt81rHUbK3Sr2uyWTKHL8v8OoUfNFRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:25:11.971722Z"},"content_sha256":"7da2b6bd70baff198ad5908cb53d3c3f72a5cb7293161beee9b77f838a35fdad","schema_version":"1.0","event_id":"sha256:7da2b6bd70baff198ad5908cb53d3c3f72a5cb7293161beee9b77f838a35fdad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GA62SKAOAFBVAEKWZ7KOK62DE6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"SDPNAL$+$: A Majorized Semismooth Newton-CG Augmented Lagrangian Method for Semidefinite Programming with Nonnegative Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Defeng Sun, Kim-Chuan Toh, Liuqin Yang","submitted_at":"2014-06-04T05:12:13Z","abstract_excerpt":"In this paper, we present a majorized semismooth Newton-CG augmented Lagrangian method, called SDPNAL$+$, for semidefinite programming (SDP) with partial or full nonnegative constraints on the matrix variable. SDPNAL$+$ is a much enhanced version of SDPNAL introduced by Zhao, Sun and Toh [SIAM Journal on Optimization, 20 (2010), pp.~1737--1765] for solving generic SDPs. SDPNAL works very efficiently for nondegenerate SDPs but may encounter numerical difficulty for degenerate ones. Here we tackle this numerical difficulty by employing a majorized semismooth Newton-CG augmented Lagrangian method"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0942","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":"2026-05-18T02:50:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zZ0mX06GYaga3Y5KWOgjRz4ruKf0eXs/RbS6H/bt9WadwE1Ev1G4MhlJtNxPhhhI3dq4aOP8Ek/nI7W8O8D+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:25:11.972469Z"},"content_sha256":"3e107acf937d4bcfd10080fd0525fbb8101ad4b08d1a3d5756772ae1126dfcd9","schema_version":"1.0","event_id":"sha256:3e107acf937d4bcfd10080fd0525fbb8101ad4b08d1a3d5756772ae1126dfcd9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GA62SKAOAFBVAEKWZ7KOK62DE6/bundle.json","state_url":"https://pith.science/pith/GA62SKAOAFBVAEKWZ7KOK62DE6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GA62SKAOAFBVAEKWZ7KOK62DE6/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":"2026-06-07T16:25:11Z","links":{"resolver":"https://pith.science/pith/GA62SKAOAFBVAEKWZ7KOK62DE6","bundle":"https://pith.science/pith/GA62SKAOAFBVAEKWZ7KOK62DE6/bundle.json","state":"https://pith.science/pith/GA62SKAOAFBVAEKWZ7KOK62DE6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GA62SKAOAFBVAEKWZ7KOK62DE6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GA62SKAOAFBVAEKWZ7KOK62DE6","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":"4a2f179c5b8ad1b4ad0cb9783d15d83468a70461b326d9f70ef9a8f5d58cd37c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-06-04T05:12:13Z","title_canon_sha256":"3b8ddb9ee15fdfbde6d803a0abf9f80f5ac74089c914cbc19510c4533a870499"},"schema_version":"1.0","source":{"id":"1406.0942","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0942","created_at":"2026-05-18T02:50:30Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0942v1","created_at":"2026-05-18T02:50:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0942","created_at":"2026-05-18T02:50:30Z"},{"alias_kind":"pith_short_12","alias_value":"GA62SKAOAFBV","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"GA62SKAOAFBVAEKW","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"GA62SKAO","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:3e107acf937d4bcfd10080fd0525fbb8101ad4b08d1a3d5756772ae1126dfcd9","target":"graph","created_at":"2026-05-18T02:50:30Z","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 present a majorized semismooth Newton-CG augmented Lagrangian method, called SDPNAL$+$, for semidefinite programming (SDP) with partial or full nonnegative constraints on the matrix variable. SDPNAL$+$ is a much enhanced version of SDPNAL introduced by Zhao, Sun and Toh [SIAM Journal on Optimization, 20 (2010), pp.~1737--1765] for solving generic SDPs. SDPNAL works very efficiently for nondegenerate SDPs but may encounter numerical difficulty for degenerate ones. Here we tackle this numerical difficulty by employing a majorized semismooth Newton-CG augmented Lagrangian method","authors_text":"Defeng Sun, Kim-Chuan Toh, Liuqin Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-06-04T05:12:13Z","title":"SDPNAL$+$: A Majorized Semismooth Newton-CG Augmented Lagrangian Method for Semidefinite Programming with Nonnegative Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0942","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":"sha256:7da2b6bd70baff198ad5908cb53d3c3f72a5cb7293161beee9b77f838a35fdad","target":"record","created_at":"2026-05-18T02:50:30Z","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":"4a2f179c5b8ad1b4ad0cb9783d15d83468a70461b326d9f70ef9a8f5d58cd37c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-06-04T05:12:13Z","title_canon_sha256":"3b8ddb9ee15fdfbde6d803a0abf9f80f5ac74089c914cbc19510c4533a870499"},"schema_version":"1.0","source":{"id":"1406.0942","kind":"arxiv","version":1}},"canonical_sha256":"303da9280e0143501156cfd4e57b4327ab028a1661106b475fd9a4a8ce7d9594","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"303da9280e0143501156cfd4e57b4327ab028a1661106b475fd9a4a8ce7d9594","first_computed_at":"2026-05-18T02:50:30.692131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:30.692131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lme8Kg8n4Cyv8RJxSn/g82WqzDgZnHmkEyI/JlGopsd4mkycFFkIqXP0atukRUSwxpgj30ENiX9xFFLtPHjlAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:30.692674Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.0942","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7da2b6bd70baff198ad5908cb53d3c3f72a5cb7293161beee9b77f838a35fdad","sha256:3e107acf937d4bcfd10080fd0525fbb8101ad4b08d1a3d5756772ae1126dfcd9"],"state_sha256":"b906348f505944fd33fc066e76adb8e2d4b632f4fa5993b8d95057fb301ef0bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Da3sLzZU3i6K0sBSkLqypqX7p9T/BQC0Np3iVqUBPAeA5W+p8CfWqz0C1LtFeBZgvevFmDH2VTlV83jl6lSMDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:25:11.976791Z","bundle_sha256":"f0f4cd6042e91ee86eeb6a7c600f18cef4c3b7cf7620f2bb4ee5f2e396b73a13"}}