TITLE: Approximation of convex hull in high dimension
QUESTION [6 upvotes]: What are efficient methods (polytime) to compute an approximation of the convex hull in high dimension (say, $30000$) for a given set of points?
Edit:
I am looking for an algorithm for getting the hyperplanes that define the convex hull, not the extreme points that are the vertices of the convex hull.

REPLY [5 votes]: This recent paper

Sartipizadeh, Hossein, and Tyrone L. Vincent. "Computing the Approximate Convex Hull in High Dimensions." arXiv:1603.04422 (2016).

includes a summary of previous work on approximate convex hulls. The time complexity of their algorithm is independent of the dimension,
and quadratic in the number of points. 
"The proposed algorithm uses a greedy method to
attempt to find the best approximation to the convex hull
for a given number of vertices."