Corpus ID: 32724082

Efficient Convex Optimization with Membership Oracles

@article{Lee2018EfficientCO,
  title={Efficient Convex Optimization with Membership Oracles},
  author={Y. Lee and Aaron Sidford and S. Vempala},
  journal={ArXiv},
  year={2018},
  volume={abs/1706.07357}
}
We consider the problem of minimizing a convex function over a convex set given access only to an evaluation oracle for the function and a membership oracle for the set. We give a simple algorithm which solves this problem with $\tilde{O}(n^2)$ oracle calls and $\tilde{O}(n^3)$ additional arithmetic operations. Using this result, we obtain more efficient reductions among the five basic oracles for convex sets and functions defined by Grotschel, Lovasz and Schrijver. 
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