Ellipsoid method

In mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions over convex sets. The ellipsoid method generates a sequence of ellipsoids whose volume uniformly decreases at every step, thus enclosing a minimizer of a convex function.

When specialized to solving feasible linear optimization problems with rational data, the ellipsoid method is an algorithm which finds an optimal solution in a number of steps that is polynomial in the input size.