Free Material Design via Semidefinite Programming: The Multiload Case with Contact Conditions
Free Material Design via Semidefinite Programming: The Multiload Case with Contact Conditions
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DOI：
10.1137/s0036144500372081
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发表时间：
1999-04
期刊：
影响因子：
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通讯作者：
A. Ben-Tal;M. Kočvara;A. Nemirovski;J. Zowe
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文献类型：
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作者：
A. Ben-Tal;M. Kočvara;A. Nemirovski;J. Zowe
自由材料设计处理的问题是，当材料分布和材料本身都可以自由变化时，找到相对于一个或多个给定载荷的最刚性结构。在最近的几篇论文中讨论了单一载荷的情况，在[M]中提出了一种有效的数值方法。科瓦拉湾Zibulevsky和J. Zowe，RAIRO模型。数学。肛交。编号，32（1998），pp. 255- 281]。我们在这里攻击多负载的情况下（在最坏的情况下理解），这是更感兴趣的应用程序，但也显着更具挑战性的理论和数值的观点。经过一系列的转换步骤，我们达到了一个问题的制定，我们可以证明存在的解决方案，一个合适的离散化导致一个半定规划问题，现代多项式时间算法的内点类型。一些数值例子证明了我们的方法的效率。
Free material design deals with the question of finding the stiffest structure with respect to one or more given loads which can be made when both the distribution of material and the material itself can freely vary. The case of one single load has been discussed in several recent papers, and an efficient numerical approach was presented in [M. Kovara, M. Zibulevsky, and J. Zowe, RAIRO Model. Math. Anal. Numer., 32 (1998), pp. 255--281]. We attack here the multiload situation (understood in the worst-case sense), which is of much more interest for applications but also significantly more challenging from both the theoretical and the numerical points of view. After a series of transformation steps we reach a problem formulation for which we can prove existence of a solution; a suitable discretization leads to a semidefinite programming problem for which modern polynomial time algorithms of interior point type are available. A number of numerical examples demonstrate the efficiency of our approach.