Efficient Convex Optimization with Membership Oracles
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 Grötschel, Lovasz and Schrijver.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2017
- DOI:
- 10.48550/arXiv.1706.07357
- arXiv:
- arXiv:1706.07357
- Bibcode:
- 2017arXiv170607357T
- Keywords:
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- Computer Science - Data Structures and Algorithms;
- Computer Science - Computational Geometry;
- Mathematics - Optimization and Control