| 多面体有限基定理的一个证明 |
| |
| 引用本文： | 谭泽光.多面体有限基定理的一个证明[J].清华大学学报(自然科学版),1988(3). |
| |
| 作者姓名： | 谭泽光 |
| |
| 作者单位： | 应用数学系 |
| |
| 摘 要： | 多面体有限基定理在最优化方法的理论研究与算法设计中起一着重要作用。本文利用 线性代数的知识和把Ｒｎ中的凸集变换成Ｒｎ＋１中凸锥的所谓齐次化方法，提供了这个 定理的一个构造性证明．同时还给出了多面体的极点、极方向和多面体的系数矩阵的关 系式。
|
| 关 键 词： | 有限基定理 多面体 极点 极方向 |
A Proof of the Finite Basis Theorem of Polyhedron |
| |
| Tan Zeguang.A Proof of the Finite Basis Theorem of Polyhedron[J].Journal of Tsinghua University(Science and Technology),1988(3). |
| |
| Authors: | Tan Zeguang |
| |
| Institution: | Department of Applied Mathematics |
| |
| Abstract: | The finite basis theorem of polyhedron plays an important part in the theoretical research and the algorithm design of optimization methods. This paper offers a constructive proof this theorem using the knowledge of linear algebra and the method called homogenization, by which a convex set in Rn is transformed into a convex cone in Rn+1, and it also gives the related expressions between the extreme points,extreme directions of polyhedron and the matrix of coefficients of polyhedron. |
| |
| Keywords: | finite basis thorem polyhedra extreme point extreme direction |
| 本文献已被 CNKI 等数据库收录！ |
