{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OZ3PTAUOTDDAQ2JZISO2L3J2OP","short_pith_number":"pith:OZ3PTAUO","schema_version":"1.0","canonical_sha256":"7676f9828e98c6086939449da5ed3a73c92e1254ae04745d1e8a07cbefe6effb","source":{"kind":"arxiv","id":"1511.04650","version":2},"attestation_state":"computed","paper":{"title":"Inverse Optimization: Closed-form Solutions, Geometry and Goodness of fit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daria Terekhov, Taewoo Lee, Timothy C. Y. Chan","submitted_at":"2015-11-15T03:31:30Z","abstract_excerpt":"In classical inverse linear optimization, one assumes a given solution is a candidate to be optimal. Real data is imperfect and noisy, so there is no guarantee this assumption is satisfied. Inspired by regression, this paper presents a unified framework for cost function estimation in linear optimization comprising a general inverse optimization model and a corresponding goodness-of-fit metric. Although our inverse optimization model is nonconvex, we derive a closed-form solution and present the geometric intuition. Our goodness-of-fit metric, $\\rho$, the coefficient of complementarity, has si"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1511.04650","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-11-15T03:31:30Z","cross_cats_sorted":[],"title_canon_sha256":"6ca6210de43f4a2ef378a7f0fdb95d62c8c311ae7cda91cf28cd43e6fc0c2cb5","abstract_canon_sha256":"5034930fd9968a58f9d458d3572598e72ad778907e2415e7ef76210c2898c0ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:53.810398Z","signature_b64":"m7ti6KKsVsgBMyqVQjJ4ZzQ01kCpmoLSAWdOPC60FpjF6HsLFajSNg7C4wLPvfRgcU7YmJgwigcdyVmai+vsAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7676f9828e98c6086939449da5ed3a73c92e1254ae04745d1e8a07cbefe6effb","last_reissued_at":"2026-05-18T00:41:53.809643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:53.809643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inverse Optimization: Closed-form Solutions, Geometry and Goodness of fit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daria Terekhov, Taewoo Lee, Timothy C. Y. Chan","submitted_at":"2015-11-15T03:31:30Z","abstract_excerpt":"In classical inverse linear optimization, one assumes a given solution is a candidate to be optimal. Real data is imperfect and noisy, so there is no guarantee this assumption is satisfied. Inspired by regression, this paper presents a unified framework for cost function estimation in linear optimization comprising a general inverse optimization model and a corresponding goodness-of-fit metric. Although our inverse optimization model is nonconvex, we derive a closed-form solution and present the geometric intuition. Our goodness-of-fit metric, $\\rho$, the coefficient of complementarity, has si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04650","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1511.04650","created_at":"2026-05-18T00:41:53.809757+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.04650v2","created_at":"2026-05-18T00:41:53.809757+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04650","created_at":"2026-05-18T00:41:53.809757+00:00"},{"alias_kind":"pith_short_12","alias_value":"OZ3PTAUOTDDA","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OZ3PTAUOTDDAQ2JZ","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OZ3PTAUO","created_at":"2026-05-18T12:29:34.919912+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OZ3PTAUOTDDAQ2JZISO2L3J2OP","json":"https://pith.science/pith/OZ3PTAUOTDDAQ2JZISO2L3J2OP.json","graph_json":"https://pith.science/api/pith-number/OZ3PTAUOTDDAQ2JZISO2L3J2OP/graph.json","events_json":"https://pith.science/api/pith-number/OZ3PTAUOTDDAQ2JZISO2L3J2OP/events.json","paper":"https://pith.science/paper/OZ3PTAUO"},"agent_actions":{"view_html":"https://pith.science/pith/OZ3PTAUOTDDAQ2JZISO2L3J2OP","download_json":"https://pith.science/pith/OZ3PTAUOTDDAQ2JZISO2L3J2OP.json","view_paper":"https://pith.science/paper/OZ3PTAUO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.04650&json=true","fetch_graph":"https://pith.science/api/pith-number/OZ3PTAUOTDDAQ2JZISO2L3J2OP/graph.json","fetch_events":"https://pith.science/api/pith-number/OZ3PTAUOTDDAQ2JZISO2L3J2OP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OZ3PTAUOTDDAQ2JZISO2L3J2OP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OZ3PTAUOTDDAQ2JZISO2L3J2OP/action/storage_attestation","attest_author":"https://pith.science/pith/OZ3PTAUOTDDAQ2JZISO2L3J2OP/action/author_attestation","sign_citation":"https://pith.science/pith/OZ3PTAUOTDDAQ2JZISO2L3J2OP/action/citation_signature","submit_replication":"https://pith.science/pith/OZ3PTAUOTDDAQ2JZISO2L3J2OP/action/replication_record"}},"created_at":"2026-05-18T00:41:53.809757+00:00","updated_at":"2026-05-18T00:41:53.809757+00:00"}