An improved ellipsoid method for solving convex differentiable optimization problems

We consider the problem of solving convex differentiable problems with simple constraints. We devise an improved ellipsoid method that relies on improved deep cuts exploiting the differentiability property of the objective function as well as the ability to compute an orthogonal projection onto the feasible set. The linear rate of convergence of the objective function values sequence is proven and several numerical results illustrate the potential advantage of this approach over the classical ellipsoid method.