Minimizing within Convex Bodies Using a Convex Hull Method
Minimizing within Convex Bodies Using a Convex Hull Method
复制标题
使用凸包方法在凸体内最小化
DOI：
--
复制
发表时间：
2005
影响因子：
3.1
通讯作者：
É. Oudet
中科院分区：
文献类型：
--
作者：
T. Lachand;É. Oudet
我们提出了在凸函数或凸体之间解决优化问题的数值方法。因此，凸度是对可允许的对象的约束，而功能不需要凸。为了解决这个问题，我们的方法混合了几何和数值算法。
我们给出了几何和分析中的经典问题引起的几种应用：亚历山德罗夫找到了处方表面功能的凸体的问题； Cheeger的子域的问题最小化了体积比表面积；牛顿的抗药性最小的问题。
特别是对于后一种应用，除了某些特定类别外，最小化器仍然未知。我们给出的解决方案比理论上的已知解决方案更好，因此表明最小化器不属于这些类别。
We present numerical methods to solve optimization problems on the space of convex functions or among convex bodies. Hence convexity is a constraint on the admissible objects, whereas the functionals are not required to be convex. To deal with this, our method mixes geometrical and numerical algorithms.
We give several applications arising from classical problems in geometry and analysis: Alexandrov's problem of finding a convex body of prescribed surface function; Cheeger's problem of a subdomain minimizing the ratio surface area on volume; Newton's problem of the body of minimal resistance.
In particular for the latter application, the minimizers are still unknown, except in some particular classes. We give approximate solutions better than the theoretical known ones, hence demonstrating that the minimizers do not belong to these classes.