A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is
We improve upon the running time for finding a point in a convex set given a separation oracle. In particular, given a separation oracle for a convex set K⊂R^n contained in a box of radius R, we show how to either find a point in K or prove that K does not contain a ball of radius ϵ using an expected O(n(nR/ϵ)) oracle evaluations and additional time O(n^3^O(1)(nR/ϵ)). This matches the oracle complexity and improves upon the O(n^ω+1(nR/ϵ)) additional time of the previous fastest algorithmarXiv:1508.04874v2 fatcat:74i57p5lardbnmstsdml66ovta