  The pressure vessel design problem is a well-known design benchmark for
validating bio-inspired optimization algorithms. However, its global optimality
is not clear and there has been no mathematical proof put forward. In this
paper, a detailed mathematical analysis of this problem is provided that proves
that 6059.714335048436 is the global minimum. The Lagrange multiplier method is
also used as an alternative proof and this method is extended to find the
global optimum of a cantilever beam design problem.
