Before revision:  By using Sum-Of-Squares (SOS) programming, branch and bound, and moment relaxations, we obtain high-quality feasible solutions for any n\inN and prove numerical global optimality for n=1,2,3. } The results obtained for n=3 show that, for any given 3^{rd} -order polynomial curve, the MINVO basis is able to obtain an enclosing simplex whose volume is 2.36 and 254.9 times smaller than the ones obtained by the Bernstein and B-Spline bases, respectively.
After revision:  By using Sum-Of-Squares (SOS) programming, branch and bound, and moment relaxations, we obtain high-quality feasible solutions for any n\inN and prove numerical global optimality for n=1,2,3. } The results obtained for n=3 show that, for any given 3^{rd} -degree polynomial curve, the MINVO basis is able to obtain an enclosing simplex whose volume is 2.36 and 254.9 times smaller than the ones obtained by the Bernstein and B-Spline bases, respectively.