A Nearly Quadratic Lower Bound for Linear Optimization over Convex Bodies in the Membership Oracle Model
Researchers prove nearly quadratic lower bounds for linear optimization over convex bodies in the membership oracle model.
The authors prove nearly quadratic lower bounds for randomized algorithms that perform linear optimization or uniform sampling over convex bodies using a membership oracle. For linear optimization, the bound matches the known nearly quadratic upper bound up to a polylog factor in the dimension. The construction improves the previous linear lower bound for uniform sampling and implies the same lower bound for volume estimation.
- Nearly quadratic lower bound for membership-oracle linear optimization.
- Bound matches the known upper bound up to a polylog factor.
- Result improves the previous linear lower bound for uniform sampling.
- The same construction also lower-bounds volume estimation.
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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.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.30215