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Weight optimization of frame structures with continuous cross-sectionparametrization is a challenging non-convex problem that has traditionally beensolved by local optimization techniques. Here, we exploit its inherentsemi-algebraic structure and adopt the Lasserre hierarchy of relaxations tocompute the global minimizers. While this hierarchy generates a naturalsequence of lower bounds, we show, under mild assumptions, how to project therelaxed solutions onto the feasible set of the original problem and thusconstruct feasible upper bounds. Based on these bounds, we develop a simplesufficient condition of global $\varepsilon$-optimality. Finally, we prove thatthe optimality gap converges to zero in the limit if the set of globalminimizers is convex. We demonstrate these results by means of two academicillustrations.

Global weight optimization of frame structures with polynomial programming