{"paper":{"title":"Polynomial iteration complexity of a path-following smoothing Newton method for symmetric cone programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A path-following smoothing Newton method achieves polynomial iteration complexity O(sqrt(ν) ln(1/ε)) for symmetric cone programming.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Rui-Jin Zhang, Ruoyu Diao, Xin-Wei Liu, Yu-Hong Dai","submitted_at":"2026-04-06T02:53:16Z","abstract_excerpt":"It has long remained open whether smoothing Newton methods (SNMs) for symmetric cone programming (SCP) admit polynomial iteration complexity. A key difficulty lies in the lack of an analogue of the self-concordant convex framework underlying interior-point methods (IPMs). In this paper, inspired by Nemirovski's self-concordant convex-concave theory, we address this open problem by introducing a reduced barrier augmented Lagrangian (BAL) function. We prove that the reduced BAL function is self-concordant convex-concave and establish that the parameterized smooth system arising in SNMs coincides"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the method is proven to achieve an iteration complexity of O( sqrt(nu) ln(1/eps) ), matching the best-known short-step bound for IPMs.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The reduced SBAL function is self-concordant convex-concave, which extends the classical self-concordant theory beyond the convex setting and enables the central-path neighborhood analysis.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A path-following smoothing Newton method for symmetric cone programming achieves O(sqrt(nu) ln(1/eps)) iteration complexity via a newly introduced self-concordant convex-concave reduced SBAL function that induces a central path.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A path-following smoothing Newton method achieves polynomial iteration complexity O(sqrt(ν) ln(1/ε)) for symmetric cone programming.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"53fda3977b4e4070481e6abe11a123a1a824bcc7fa85e06321641d24d206a3b2"},"source":{"id":"2604.04376","kind":"arxiv","version":2},"verdict":{"id":"4c96c8ae-823d-404f-b7ab-3cfffda244d2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T20:16:36.853528Z","strongest_claim":"the method is proven to achieve an iteration complexity of O( sqrt(nu) ln(1/eps) ), matching the best-known short-step bound for IPMs.","one_line_summary":"A path-following smoothing Newton method for symmetric cone programming achieves O(sqrt(nu) ln(1/eps)) iteration complexity via a newly introduced self-concordant convex-concave reduced SBAL function that induces a central path.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The reduced SBAL function is self-concordant convex-concave, which extends the classical self-concordant theory beyond the convex setting and enables the central-path neighborhood analysis.","pith_extraction_headline":"A path-following smoothing Newton method achieves polynomial iteration complexity O(sqrt(ν) ln(1/ε)) for symmetric cone programming."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.04376/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":2,"snapshot_sha256":"b0f9189361b3899c52f568f17b5c8dc5393a9a3eb09a6bfca0a3f94b1968b65a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}