Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.30215

Author: Vempala, Santosh S.

Institution: Georgia Institute of Technology

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Collaborative Research: AF: Medium: Fundamental Challenges in Discrete and Continuous Optimization

OpenAlex ID: W7214403325

Cites: 1

Cited by: 3

Related to: 10