  Weight optimization of frame structures with continuous cross-section
parametrization is a challenging non-convex problem that has traditionally been
solved by local optimization techniques. Here, we exploit its inherent
semi-algebraic structure and adopt the Lasserre hierarchy of relaxations to
compute the global minimizers. While this hierarchy generates a natural
sequence of lower bounds, we show, under mild assumptions, how to project the
relaxed solutions onto the feasible set of the original problem and thus
construct feasible upper bounds. Based on these bounds, we develop a simple
sufficient condition of global $\varepsilon$-optimality. Finally, we prove that
the optimality gap converges to zero in the limit if the set of global
minimizers is convex. We demonstrate these results by means of two academic
illustrations.
