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arXiv · 1706.07357

Efficient Convex Optimization with Membership Oracles

Yin Tat Lee·Aaron Sidford·Santosh S. Vempala
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Abstract

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 Gr\"otschel, Lovasz and Schrijver.

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Yin Tat Lee, Aaron Sidford, Santosh S. Vempala. 2017-06-22. Efficient Convex Optimization with Membership Oracles. https://arxiv.org/abs/1706.07357

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