{"paper":{"title":"A Backstepping Framework for Unconstrained Accelerated Optimization Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chao Xu, Jiaxu Liu, Song Chen","submitted_at":"2026-06-26T05:11:16Z","abstract_excerpt":"This paper introduces a control-theoretic perspective on unconstrained optimization algorithms using the backstepping methods. We model the optimization process as an augmented strict-feedback system given by $\\dot{x}_1 = x_2$, $\\dot{x}_2 = u$, and $\\dot{z} = q(x_1,z)$, with a regulated output $y = \\nabla f(x_1)$. This formulation recasts the development of unconstrained optimization algorithms as a feedback control problem, where the goal is to design the input $u$ to ensure $y(t) \\to 0$. By employing backstepping, we recursively synthesize the actual feedback law $u$ after initially selectin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27722","kind":"arxiv","version":1},"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/2606.27722/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"}