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 eprints
 Pub Date:
 June 2017
 arXiv:
 arXiv:1706.07357
 Bibcode:
 2017arXiv170607357T
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Geometry;
 Mathematics  Optimization and Control