[Submitted on 24 Sep 2026 (v1), last revised 30 Oct 2026 (this version, v2)]
Abstract:We prove nearly quadratic lower bounds for randomized algorithms for linear optimization and uniform sampling over convex bodies in the membership oracle model. For linear optimization, this matches the known nearly quadratic upper bound up to a polylog factor in the dimension. For uniform sampling, this improves on the previous linear lower bound. Our construction also implies the same lower bound for volume estimation.
Submission history
From: Santosh Vempala [view email]
[v1] Thu, 24 Sep 2026 17:45:58 UTC (24 KB)
[v2] Fri, 30 Oct 2026 17:45:38 UTC (150 KB)
