mlsanityData to 14 Oct 2026

A Nearly Quadratic Lower Bound for Linear Optimization over Convex Bodies in the Membership Oracle Model

arXiv 2609.30215 ↗First posted 24 Sep 2026cs.DS cs.LG math.FAcited by 1

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Abstract (arXiv)

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.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 4 of its 26 references that are in the map. First posted on arXiv 24 Sep 2026.

Builds on

4 of 26 references.

References · 4

  1. 2018Convex optimization using quantum oraclescited by 19
  2. 2018Quantum algorithms and lower bounds for convex optimizationcited by 15
  3. 2020Reducing Isotropy and Volume to KLS: Faster Rounding and Volume Algorithmscited by 9
  4. 2026Closing the Oracle-Complexity Gap in Derivative-Free Convex Optimization: A Near-Quadratic Lower Bound from Exact Function Valuescited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Lower Bounds for Parallel Diffusion Samplingcited by 0