{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:JACLDDRFM3Z7LY53VXROT2VAIO","short_pith_number":"pith:JACLDDRF","schema_version":"1.0","canonical_sha256":"4804b18e2566f3f5e3bbade2e9eaa043815b77056980e81a569a01d2ce9cb9bd","source":{"kind":"arxiv","id":"1207.6710","version":2},"attestation_state":"computed","paper":{"title":"Four strategies to develop canonical dual algorithms for global optimization problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Xiaojun Zhou","submitted_at":"2012-07-28T16:39:56Z","abstract_excerpt":"The canonical duality theory has provided with a unified analytic solution to a range of discrete and continuous problems in global optimization, which can transform a nonconvex primal problem to a concave maximization dual problem over a convex domain without duality gap. This paper shows that under certain conditions, this canonical dual problem is equivalent to the standard semi-definite programming (SDP) problem, which can be solved by well-developed software packages. In order to avoid certain difficulties of using the SDP method, four strategies are proposed based on unconstrained approa"},"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":"1207.6710","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-07-28T16:39:56Z","cross_cats_sorted":[],"title_canon_sha256":"8a42b457308940c483713874db4dd36e9898c186432e7bdb1b58fb0df3a95ad4","abstract_canon_sha256":"283dfcfb4e916ee08971a1e0f727278f1439d192bd31bd4f5b3ccab537841a14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:13.444914Z","signature_b64":"T4+HnSA3zvbDUv5veJrDEMUQxN89BnwynZRZx+ypu5Rf04WSVWHpXq6+CXtI7GDylQJz7Cj91eljmZIlHpShAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4804b18e2566f3f5e3bbade2e9eaa043815b77056980e81a569a01d2ce9cb9bd","last_reissued_at":"2026-05-18T03:44:13.444435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:13.444435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Four strategies to develop canonical dual algorithms for global optimization problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Xiaojun Zhou","submitted_at":"2012-07-28T16:39:56Z","abstract_excerpt":"The canonical duality theory has provided with a unified analytic solution to a range of discrete and continuous problems in global optimization, which can transform a nonconvex primal problem to a concave maximization dual problem over a convex domain without duality gap. This paper shows that under certain conditions, this canonical dual problem is equivalent to the standard semi-definite programming (SDP) problem, which can be solved by well-developed software packages. In order to avoid certain difficulties of using the SDP method, four strategies are proposed based on unconstrained approa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6710","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":"1207.6710","created_at":"2026-05-18T03:44:13.444510+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.6710v2","created_at":"2026-05-18T03:44:13.444510+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6710","created_at":"2026-05-18T03:44:13.444510+00:00"},{"alias_kind":"pith_short_12","alias_value":"JACLDDRFM3Z7","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"JACLDDRFM3Z7LY53","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"JACLDDRF","created_at":"2026-05-18T12:27:11.947152+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/JACLDDRFM3Z7LY53VXROT2VAIO","json":"https://pith.science/pith/JACLDDRFM3Z7LY53VXROT2VAIO.json","graph_json":"https://pith.science/api/pith-number/JACLDDRFM3Z7LY53VXROT2VAIO/graph.json","events_json":"https://pith.science/api/pith-number/JACLDDRFM3Z7LY53VXROT2VAIO/events.json","paper":"https://pith.science/paper/JACLDDRF"},"agent_actions":{"view_html":"https://pith.science/pith/JACLDDRFM3Z7LY53VXROT2VAIO","download_json":"https://pith.science/pith/JACLDDRFM3Z7LY53VXROT2VAIO.json","view_paper":"https://pith.science/paper/JACLDDRF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.6710&json=true","fetch_graph":"https://pith.science/api/pith-number/JACLDDRFM3Z7LY53VXROT2VAIO/graph.json","fetch_events":"https://pith.science/api/pith-number/JACLDDRFM3Z7LY53VXROT2VAIO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JACLDDRFM3Z7LY53VXROT2VAIO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JACLDDRFM3Z7LY53VXROT2VAIO/action/storage_attestation","attest_author":"https://pith.science/pith/JACLDDRFM3Z7LY53VXROT2VAIO/action/author_attestation","sign_citation":"https://pith.science/pith/JACLDDRFM3Z7LY53VXROT2VAIO/action/citation_signature","submit_replication":"https://pith.science/pith/JACLDDRFM3Z7LY53VXROT2VAIO/action/replication_record"}},"created_at":"2026-05-18T03:44:13.444510+00:00","updated_at":"2026-05-18T03:44:13.444510+00:00"}