{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5VJFSG74PRYZU6BED2U6USJSRQ","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":"a9f55e728f39e902c1ad2831c923bd943d43d5b8fc9ea2867f352021d3de59db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-31T10:16:52Z","title_canon_sha256":"24009aa90484c042565d54ee2a5171b57f4610cad34e2baba90d818a9bbe84ef"},"schema_version":"1.0","source":{"id":"1210.8284","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.8284","created_at":"2026-05-18T03:41:55Z"},{"alias_kind":"arxiv_version","alias_value":"1210.8284v1","created_at":"2026-05-18T03:41:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.8284","created_at":"2026-05-18T03:41:55Z"},{"alias_kind":"pith_short_12","alias_value":"5VJFSG74PRYZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5VJFSG74PRYZU6BE","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5VJFSG74","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:d866fa8f6b4f2aea68a8442e6746665790a928c8c88b5ea9158dc27a491fe662","target":"graph","created_at":"2026-05-18T03:41:55Z","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 establish hardness and approximation results for various $L_p$-ball constrained homogeneous polynomial optimization problems, where $p \\in [2,\\infty]$. Specifically, we prove that for any given $d \\ge 3$ and $p \\in [2,\\infty]$, both the problem of optimizing a degree-$d$ homogeneous polynomial over the $L_p$-ball and the problem of optimizing a degree-$d$ multilinear form (regardless of its super-symmetry) over $L_p$-balls are NP-hard. On the other hand, we show that these problems can be approximated to within a factor of $\\Omega((\\log n)^{(d-2)/p} \\big/ n^{d/2-1})$ in deter","authors_text":"Anthony Man-Cho So, Ke Hou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-31T10:16:52Z","title":"Hardness and Approximation Results for $L_p$-Ball Constrained Homogeneous Polynomial Optimization Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8284","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:e15a7b916fa8a0f1f00b63c339ef4fc89fcbd5595e2922286c3d1d0ec7dc05a8","target":"record","created_at":"2026-05-18T03:41:55Z","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":"a9f55e728f39e902c1ad2831c923bd943d43d5b8fc9ea2867f352021d3de59db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-31T10:16:52Z","title_canon_sha256":"24009aa90484c042565d54ee2a5171b57f4610cad34e2baba90d818a9bbe84ef"},"schema_version":"1.0","source":{"id":"1210.8284","kind":"arxiv","version":1}},"canonical_sha256":"ed52591bfc7c719a78241ea9ea49328c202584566dea2ab1d4a9e0ce7a621bbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed52591bfc7c719a78241ea9ea49328c202584566dea2ab1d4a9e0ce7a621bbe","first_computed_at":"2026-05-18T03:41:55.452283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:55.452283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LM5wyPeMLwCc+UQ0bK5bDwnl/3otKO0BzpLIKwToK7KYni4aKaIugWq8si7yzga8FGLK4b2df28ccdUP9lGaCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:55.453060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.8284","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e15a7b916fa8a0f1f00b63c339ef4fc89fcbd5595e2922286c3d1d0ec7dc05a8","sha256:d866fa8f6b4f2aea68a8442e6746665790a928c8c88b5ea9158dc27a491fe662"],"state_sha256":"86ade3bfd1a9f00704cb45005573297add8b25af575742aa31564607b65b11ba"}