{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:NZI3H6H6R4XMTHQR3BRPJ5LTIX","short_pith_number":"pith:NZI3H6H6","canonical_record":{"source":{"id":"2007.13545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-07-19T07:15:37Z","cross_cats_sorted":[],"title_canon_sha256":"76c0bbd8a02a8fb1716e7cb44a4b6cc5a9fce37f460e635105f852c27a5c2003","abstract_canon_sha256":"e42adedd5323fa97cac377c171b738d00b8dbb11a5840009b7cfc2ace08441ce"},"schema_version":"1.0"},"canonical_sha256":"6e51b3f8fe8f2ec99e11d862f4f57345d09be7e384bf7afb881eaf85e1888612","source":{"kind":"arxiv","id":"2007.13545","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.13545","created_at":"2026-07-05T01:22:25Z"},{"alias_kind":"arxiv_version","alias_value":"2007.13545v1","created_at":"2026-07-05T01:22:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.13545","created_at":"2026-07-05T01:22:25Z"},{"alias_kind":"pith_short_12","alias_value":"NZI3H6H6R4XM","created_at":"2026-07-05T01:22:25Z"},{"alias_kind":"pith_short_16","alias_value":"NZI3H6H6R4XMTHQR","created_at":"2026-07-05T01:22:25Z"},{"alias_kind":"pith_short_8","alias_value":"NZI3H6H6","created_at":"2026-07-05T01:22:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:NZI3H6H6R4XMTHQR3BRPJ5LTIX","target":"record","payload":{"canonical_record":{"source":{"id":"2007.13545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-07-19T07:15:37Z","cross_cats_sorted":[],"title_canon_sha256":"76c0bbd8a02a8fb1716e7cb44a4b6cc5a9fce37f460e635105f852c27a5c2003","abstract_canon_sha256":"e42adedd5323fa97cac377c171b738d00b8dbb11a5840009b7cfc2ace08441ce"},"schema_version":"1.0"},"canonical_sha256":"6e51b3f8fe8f2ec99e11d862f4f57345d09be7e384bf7afb881eaf85e1888612","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:22:25.292212Z","signature_b64":"h+RbSv/Hz22Epz0+YdinDrNKLz9MUjYQ8/r5Cnwdb/g+wslo81IAEXG31RlCqsM06b1nHYhPCWpgjQaCN9GWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e51b3f8fe8f2ec99e11d862f4f57345d09be7e384bf7afb881eaf85e1888612","last_reissued_at":"2026-07-05T01:22:25.291761Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:22:25.291761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.13545","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":"2026-07-05T01:22:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2oOekj2HkKslZlk2og8vbwHNSXdbEwfl1TLycB4cKMepHPl31CHnEV4bTP3hik54rUBB/s2jc5+5/KIJbJYLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T16:23:41.254974Z"},"content_sha256":"b6ddc3e236c64de637253c98482ff190595cb9225fc12b18ef7cffda5fb44199","schema_version":"1.0","event_id":"sha256:b6ddc3e236c64de637253c98482ff190595cb9225fc12b18ef7cffda5fb44199"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:NZI3H6H6R4XMTHQR3BRPJ5LTIX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tutorials on Advanced Optimization Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Wei Wei","submitted_at":"2020-07-19T07:15:37Z","abstract_excerpt":"This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization, and equilibrium/game problems. It discusses how to reformulate a difficult (non-convex, multi-agent, min-max) problem to a solver-compatible form (semidefinite program, mixed-integer linear program) via convexification, linearization, and decomposition, so the original problem can be reliably solved by commercial/open-source software. Fundamental algorithms"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.13545","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.13545/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:22:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Cqq0mPYdoqP+cDgwOHycGwoIzivowOpNMVaY4Q7oo+Nbb7zsxzU+82GtRoK+Z0nFyJEVXz83//mkf+RxyZOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T16:23:41.255870Z"},"content_sha256":"ebf9b8cb4103836c33ee0bcb872ee348a8699a41761d0fdfa3f53ee4cc0260d9","schema_version":"1.0","event_id":"sha256:ebf9b8cb4103836c33ee0bcb872ee348a8699a41761d0fdfa3f53ee4cc0260d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZI3H6H6R4XMTHQR3BRPJ5LTIX/bundle.json","state_url":"https://pith.science/pith/NZI3H6H6R4XMTHQR3BRPJ5LTIX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZI3H6H6R4XMTHQR3BRPJ5LTIX/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":"2026-08-18T16:23:41Z","links":{"resolver":"https://pith.science/pith/NZI3H6H6R4XMTHQR3BRPJ5LTIX","bundle":"https://pith.science/pith/NZI3H6H6R4XMTHQR3BRPJ5LTIX/bundle.json","state":"https://pith.science/pith/NZI3H6H6R4XMTHQR3BRPJ5LTIX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZI3H6H6R4XMTHQR3BRPJ5LTIX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:NZI3H6H6R4XMTHQR3BRPJ5LTIX","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":"e42adedd5323fa97cac377c171b738d00b8dbb11a5840009b7cfc2ace08441ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-07-19T07:15:37Z","title_canon_sha256":"76c0bbd8a02a8fb1716e7cb44a4b6cc5a9fce37f460e635105f852c27a5c2003"},"schema_version":"1.0","source":{"id":"2007.13545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.13545","created_at":"2026-07-05T01:22:25Z"},{"alias_kind":"arxiv_version","alias_value":"2007.13545v1","created_at":"2026-07-05T01:22:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.13545","created_at":"2026-07-05T01:22:25Z"},{"alias_kind":"pith_short_12","alias_value":"NZI3H6H6R4XM","created_at":"2026-07-05T01:22:25Z"},{"alias_kind":"pith_short_16","alias_value":"NZI3H6H6R4XMTHQR","created_at":"2026-07-05T01:22:25Z"},{"alias_kind":"pith_short_8","alias_value":"NZI3H6H6","created_at":"2026-07-05T01:22:25Z"}],"graph_snapshots":[{"event_id":"sha256:ebf9b8cb4103836c33ee0bcb872ee348a8699a41761d0fdfa3f53ee4cc0260d9","target":"graph","created_at":"2026-07-05T01:22:25Z","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/2007.13545/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization, and equilibrium/game problems. It discusses how to reformulate a difficult (non-convex, multi-agent, min-max) problem to a solver-compatible form (semidefinite program, mixed-integer linear program) via convexification, linearization, and decomposition, so the original problem can be reliably solved by commercial/open-source software. Fundamental algorithms","authors_text":"Wei Wei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-07-19T07:15:37Z","title":"Tutorials on Advanced Optimization Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.13545","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:b6ddc3e236c64de637253c98482ff190595cb9225fc12b18ef7cffda5fb44199","target":"record","created_at":"2026-07-05T01:22:25Z","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":"e42adedd5323fa97cac377c171b738d00b8dbb11a5840009b7cfc2ace08441ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-07-19T07:15:37Z","title_canon_sha256":"76c0bbd8a02a8fb1716e7cb44a4b6cc5a9fce37f460e635105f852c27a5c2003"},"schema_version":"1.0","source":{"id":"2007.13545","kind":"arxiv","version":1}},"canonical_sha256":"6e51b3f8fe8f2ec99e11d862f4f57345d09be7e384bf7afb881eaf85e1888612","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e51b3f8fe8f2ec99e11d862f4f57345d09be7e384bf7afb881eaf85e1888612","first_computed_at":"2026-07-05T01:22:25.291761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:22:25.291761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h+RbSv/Hz22Epz0+YdinDrNKLz9MUjYQ8/r5Cnwdb/g+wslo81IAEXG31RlCqsM06b1nHYhPCWpgjQaCN9GWAA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:22:25.292212Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.13545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6ddc3e236c64de637253c98482ff190595cb9225fc12b18ef7cffda5fb44199","sha256:ebf9b8cb4103836c33ee0bcb872ee348a8699a41761d0fdfa3f53ee4cc0260d9"],"state_sha256":"3c99e2990f4266d319f40348beeddb0409da547374843b41c6539b34f424e48e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RQIHGp2gNTmINwcjB3KPNJO7xWyhb/YdN9KZmqfasrHFZSVYC0KeVB0q1cB8qR73KsbfHPPhEQI+0mFKdtVGDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T16:23:41.261439Z","bundle_sha256":"9034414ae7184a8f1ddeece00a9ab6f2041a3e0c1cecdca5c9596fe673ef1ace"}}