I am trying to find a way to draw random points from convex sets in arbitrary dimensions. In particular, the sets are described by a continuous, differentiable, and quasiconvex function g such that the sets are given by S = {x in R_+^n: g(x) = 0}. So the problem is finding a random point in S uniformly distributed on S, i.e. each point in S is drawn with the same probability.

I reckon that the above problem is too general to admit an easy solution. But for my purposes, it would already be sufficient to find a way to randomly draw a point from sets given by {x in R_+^n: Sum a_i x_i^r = w from i=1 to n}, with r >= 1 (apparently, these sets are the boundaries of so called "superellipsoids").

Now, I do know how to draw random points uniformly distributed on spheres. I also know how to use that knowledge to draw random points uniformly distributed on ellipsoids, using an acception-rejection algorithm. But I am clueless about how to tackle the more general (second) problem described above.

Any help would be appreciated.

(Note: This is a repost from http://www.mathhelpforum.com where nobody could help me.

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