  Optimization of frame structures is formulated as a~non-convex optimization
problem, which is currently solved to local optimality. In this contribution,
we investigate four optimization approaches: (i) general non-linear
optimization, (ii) optimality criteria method, (iii) non-linear semidefinite
programming, and (iv) polynomial optimization. We show that polynomial
optimization solves the frame structure optimization to global optimality by
building the (moment-sums-of-squares) hierarchy of convex linear semidefinite
programming problems, and it also provides guaranteed lower and upper bounds on
optimal design. Finally, we solve three sample optimization problems and
conclude that the local optimization approaches may indeed converge to local
optima, without any solution quality measure, or even to infeasible points.
These issues are readily overcome by using polynomial optimization, which
exhibits a finite convergence, at the prize of higher computational demands.
