论文标题
通过多项式编程对框架结构的全球重量优化
Global weight optimization of frame structures with polynomial programming
论文作者
论文摘要
具有连续横截面参数化的框架结构的重量优化是一个具有挑战性的非凸问题，传统上已经通过局部优化技术解决了。在这里，我们利用其固有的半代数结构，并采用放松的宽松等级来计算全球最小化器。尽管该层次结构产生了自然的下限序列，但我们在轻度假设下显示了如何将松弛的溶液投射到可行的原始问题集上，从而构建了可行的上限。基于这些界限，我们开发了全局$ \ varepsilon $ - 最佳性的简单条件。最后，我们证明，如果全局最小化器的集合是凸，那么最佳差距将其收敛到零。我们通过两个学术插图来证明这些结果。
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.
