{"paper":{"title":"Fixed Point Computation: Beating Brute Force with Smoothed Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG"],"primary_cat":"cs.GT","authors_text":"Constantinos Daskalakis, Idan Attias, Manolis Zampetakis, Rui Yao, Yuval Dagan","submitted_at":"2025-01-18T21:32:26Z","abstract_excerpt":"We propose a new algorithm that finds an $\\varepsilon$-approximate fixed point of a smooth function from the $n$-dimensional $\\ell_2$ unit ball to itself. We use the general framework of finding approximate solutions to a variational inequality, a problem that subsumes fixed point computation and the computation of a Nash Equilibrium. The algorithm's runtime is bounded by $e^{O(n)}/\\varepsilon$, under the smoothed-analysis framework. This is the first known algorithm in such a generality whose runtime is faster than $(1/\\varepsilon)^{O(n)}$, which is a time that suffices for an exhaustive sear"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.10884","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/2501.10884/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"}