{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3NFJK6MVNAPGTYLYJNXI66STYC","short_pith_number":"pith:3NFJK6MV","canonical_record":{"source":{"id":"1702.03262","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-10T17:30:50Z","cross_cats_sorted":[],"title_canon_sha256":"bd25472ac4233c9fd1bb7c6da7fa9fc6eb360a0d22d95d8e1e7b67c0c1869cc7","abstract_canon_sha256":"e878da4ac518f7b3e170cf4ef504fbefa78101d7a1972bef4e106cbca1403341"},"schema_version":"1.0"},"canonical_sha256":"db4a957995681e69e1784b6e8f7a53c0abaf9c9c8810640c6dc073552c9c73d5","source":{"kind":"arxiv","id":"1702.03262","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03262","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03262v3","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03262","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"pith_short_12","alias_value":"3NFJK6MVNAPG","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3NFJK6MVNAPGTYLY","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3NFJK6MV","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3NFJK6MVNAPGTYLYJNXI66STYC","target":"record","payload":{"canonical_record":{"source":{"id":"1702.03262","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-10T17:30:50Z","cross_cats_sorted":[],"title_canon_sha256":"bd25472ac4233c9fd1bb7c6da7fa9fc6eb360a0d22d95d8e1e7b67c0c1869cc7","abstract_canon_sha256":"e878da4ac518f7b3e170cf4ef504fbefa78101d7a1972bef4e106cbca1403341"},"schema_version":"1.0"},"canonical_sha256":"db4a957995681e69e1784b6e8f7a53c0abaf9c9c8810640c6dc073552c9c73d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:01.244828Z","signature_b64":"ecOwuR++PTagA97zxYX5cbKrOFgAgisUu7el1Jt0S44DgRk9Qi1K7JeMFxn/hqpLAroHd+ecpUdxd+96nJhxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db4a957995681e69e1784b6e8f7a53c0abaf9c9c8810640c6dc073552c9c73d5","last_reissued_at":"2026-05-18T00:45:01.244271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:01.244271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.03262","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:45:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l1qy3JiFWKH26R5XoRBBNzcIAD62gj0tEnbHGMeUWeDl8QNklstWIO1ZjKzfM7RmCciy5fqWQUiW6m6JVyc4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T13:48:48.076468Z"},"content_sha256":"2b6331b4bfd87da9baff51ff6003b3a00403e29226a1eaa0dab484a5cc84e16c","schema_version":"1.0","event_id":"sha256:2b6331b4bfd87da9baff51ff6003b3a00403e29226a1eaa0dab484a5cc84e16c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3NFJK6MVNAPGTYLYJNXI66STYC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quadratic growth conditions for convex matrix optimization problems associated with spectral functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chao Ding, Xinyuan Zhao, Ying Cui","submitted_at":"2017-02-10T17:30:50Z","abstract_excerpt":"In this paper, we provide two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex symmetric and non-symmetric matrix optimization problems regularized by nonsmooth spectral functions. These sufficient conditions are derived via the study of the $\\mathcal{C}^2$-cone reducibility of spectral functions and the metric subregularity of their subdifferentials, respectively. As an application, we demonstrate how quadratic growth conditions are used to guarantee the desirable fast convergence rates of the augmented Lagrangian methods (ALM) for s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03262","kind":"arxiv","version":3},"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":"2026-05-18T00:45:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rUhqn5zU+dOlej+HK80yIuSI3wQcKLQdskMaW/vAPflToXEZuk0B+CrQSr4EKuuExEoMOkZEW0GSl9rBySo8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T13:48:48.076815Z"},"content_sha256":"57bf70851735973d1cb52266b29a09002a622ad1a4b3d80a1f4c9b1f9ac9aebd","schema_version":"1.0","event_id":"sha256:57bf70851735973d1cb52266b29a09002a622ad1a4b3d80a1f4c9b1f9ac9aebd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3NFJK6MVNAPGTYLYJNXI66STYC/bundle.json","state_url":"https://pith.science/pith/3NFJK6MVNAPGTYLYJNXI66STYC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3NFJK6MVNAPGTYLYJNXI66STYC/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":"2026-06-04T13:48:48Z","links":{"resolver":"https://pith.science/pith/3NFJK6MVNAPGTYLYJNXI66STYC","bundle":"https://pith.science/pith/3NFJK6MVNAPGTYLYJNXI66STYC/bundle.json","state":"https://pith.science/pith/3NFJK6MVNAPGTYLYJNXI66STYC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3NFJK6MVNAPGTYLYJNXI66STYC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3NFJK6MVNAPGTYLYJNXI66STYC","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":"e878da4ac518f7b3e170cf4ef504fbefa78101d7a1972bef4e106cbca1403341","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-10T17:30:50Z","title_canon_sha256":"bd25472ac4233c9fd1bb7c6da7fa9fc6eb360a0d22d95d8e1e7b67c0c1869cc7"},"schema_version":"1.0","source":{"id":"1702.03262","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03262","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03262v3","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03262","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"pith_short_12","alias_value":"3NFJK6MVNAPG","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3NFJK6MVNAPGTYLY","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3NFJK6MV","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:57bf70851735973d1cb52266b29a09002a622ad1a4b3d80a1f4c9b1f9ac9aebd","target":"graph","created_at":"2026-05-18T00:45:01Z","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 provide two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex symmetric and non-symmetric matrix optimization problems regularized by nonsmooth spectral functions. These sufficient conditions are derived via the study of the $\\mathcal{C}^2$-cone reducibility of spectral functions and the metric subregularity of their subdifferentials, respectively. As an application, we demonstrate how quadratic growth conditions are used to guarantee the desirable fast convergence rates of the augmented Lagrangian methods (ALM) for s","authors_text":"Chao Ding, Xinyuan Zhao, Ying Cui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-10T17:30:50Z","title":"Quadratic growth conditions for convex matrix optimization problems associated with spectral functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03262","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":"sha256:2b6331b4bfd87da9baff51ff6003b3a00403e29226a1eaa0dab484a5cc84e16c","target":"record","created_at":"2026-05-18T00:45:01Z","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":"e878da4ac518f7b3e170cf4ef504fbefa78101d7a1972bef4e106cbca1403341","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-10T17:30:50Z","title_canon_sha256":"bd25472ac4233c9fd1bb7c6da7fa9fc6eb360a0d22d95d8e1e7b67c0c1869cc7"},"schema_version":"1.0","source":{"id":"1702.03262","kind":"arxiv","version":3}},"canonical_sha256":"db4a957995681e69e1784b6e8f7a53c0abaf9c9c8810640c6dc073552c9c73d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db4a957995681e69e1784b6e8f7a53c0abaf9c9c8810640c6dc073552c9c73d5","first_computed_at":"2026-05-18T00:45:01.244271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:01.244271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ecOwuR++PTagA97zxYX5cbKrOFgAgisUu7el1Jt0S44DgRk9Qi1K7JeMFxn/hqpLAroHd+ecpUdxd+96nJhxAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:01.244828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03262","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b6331b4bfd87da9baff51ff6003b3a00403e29226a1eaa0dab484a5cc84e16c","sha256:57bf70851735973d1cb52266b29a09002a622ad1a4b3d80a1f4c9b1f9ac9aebd"],"state_sha256":"bd6413411f3be4d5a966a4d6cb942252da86550e2d453fd0aa57fcb4abf4b12a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"slJo/MZLdyqoVEwdTR2pS7KOShLPK3OaoncfddyEPEiry5ixEfgg/dGX83/gZ3hRd6TTUFeOuRHRvtca81LYBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T13:48:48.078958Z","bundle_sha256":"feb79183faf06ddcbb4cf313c3d696715896b8a62d1d0dfd81bf9f866c3d1539"}}