{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:TELJ53MCQR3NS3YTNUNU5L56UJ","short_pith_number":"pith:TELJ53MC","schema_version":"1.0","canonical_sha256":"99169eed828476d96f136d1b4eafbea27480308b507161cf8f0379cc461095c6","source":{"kind":"arxiv","id":"2310.01784","version":2},"attestation_state":"computed","paper":{"title":"On Squared-Variable Formulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Lijun Ding, Stephen J. Wright","submitted_at":"2023-10-03T04:22:09Z","abstract_excerpt":"We revisit a formulation technique for inequality constrained optimization problems that has been known for decades: the substitution of squared variables for nonnegative variables. Using this technique, inequality constraints are converted to equality constraints via the introduction of a squared-slack variable. Such formulations have the superficial advantage that inequality constraints can be dispensed with altogether. But there are clear disadvantages, not least being that first-order optimal points for the squared-variable reformulation may not correspond to first-order optimal points for"},"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":"2310.01784","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-10-03T04:22:09Z","cross_cats_sorted":[],"title_canon_sha256":"2b181b151acdd36252763e95bc438e997b6293580baed66f29d47bc2510b0ec0","abstract_canon_sha256":"e7faa5a67a4eca85093744cacf68e7beea4f55cc57cb7c7fa5f0b2f0c4665507"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:31:42.214214Z","signature_b64":"2CGceN5cJBEV8QkPfBm46gKrdri/KwntPIrj9PEvodP+Noi7hgAI0Scs5lCm2IzwyiY6vMiZWZtrvoehr2/GBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99169eed828476d96f136d1b4eafbea27480308b507161cf8f0379cc461095c6","last_reissued_at":"2026-07-05T09:31:42.213782Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:31:42.213782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Squared-Variable Formulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Lijun Ding, Stephen J. Wright","submitted_at":"2023-10-03T04:22:09Z","abstract_excerpt":"We revisit a formulation technique for inequality constrained optimization problems that has been known for decades: the substitution of squared variables for nonnegative variables. Using this technique, inequality constraints are converted to equality constraints via the introduction of a squared-slack variable. Such formulations have the superficial advantage that inequality constraints can be dispensed with altogether. But there are clear disadvantages, not least being that first-order optimal points for the squared-variable reformulation may not correspond to first-order optimal points for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.01784","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.01784/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2310.01784","created_at":"2026-07-05T09:31:42.213838+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.01784v2","created_at":"2026-07-05T09:31:42.213838+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.01784","created_at":"2026-07-05T09:31:42.213838+00:00"},{"alias_kind":"pith_short_12","alias_value":"TELJ53MCQR3N","created_at":"2026-07-05T09:31:42.213838+00:00"},{"alias_kind":"pith_short_16","alias_value":"TELJ53MCQR3NS3YT","created_at":"2026-07-05T09:31:42.213838+00:00"},{"alias_kind":"pith_short_8","alias_value":"TELJ53MC","created_at":"2026-07-05T09:31:42.213838+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.15264","citing_title":"On exploration of an interior mirror descent flow for stochastic nonconvex constrained problem","ref_index":27,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TELJ53MCQR3NS3YTNUNU5L56UJ","json":"https://pith.science/pith/TELJ53MCQR3NS3YTNUNU5L56UJ.json","graph_json":"https://pith.science/api/pith-number/TELJ53MCQR3NS3YTNUNU5L56UJ/graph.json","events_json":"https://pith.science/api/pith-number/TELJ53MCQR3NS3YTNUNU5L56UJ/events.json","paper":"https://pith.science/paper/TELJ53MC"},"agent_actions":{"view_html":"https://pith.science/pith/TELJ53MCQR3NS3YTNUNU5L56UJ","download_json":"https://pith.science/pith/TELJ53MCQR3NS3YTNUNU5L56UJ.json","view_paper":"https://pith.science/paper/TELJ53MC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.01784&json=true","fetch_graph":"https://pith.science/api/pith-number/TELJ53MCQR3NS3YTNUNU5L56UJ/graph.json","fetch_events":"https://pith.science/api/pith-number/TELJ53MCQR3NS3YTNUNU5L56UJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TELJ53MCQR3NS3YTNUNU5L56UJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TELJ53MCQR3NS3YTNUNU5L56UJ/action/storage_attestation","attest_author":"https://pith.science/pith/TELJ53MCQR3NS3YTNUNU5L56UJ/action/author_attestation","sign_citation":"https://pith.science/pith/TELJ53MCQR3NS3YTNUNU5L56UJ/action/citation_signature","submit_replication":"https://pith.science/pith/TELJ53MCQR3NS3YTNUNU5L56UJ/action/replication_record"}},"created_at":"2026-07-05T09:31:42.213838+00:00","updated_at":"2026-07-05T09:31:42.213838+00:00"}