Farkas引理在张量结构下的讨论

Discussion of Farkas’ Lemma in Tensor Structure

Farkas引理在优化理论体系中具有十分重要的应用,张量是一种多维数组,在高维图像分析、超图聚类等方面具有重要的应用。本文研究张量结构下的Farkas引理,在张量的理论体系下对Farkas引理进行推广,通过引入非空闭凸集的概念及相关知识,利用点与闭凸集的分离定理,得到了张量结构下的Farkas引理。

Farkas’ lemma holds significant importance in the system of optimization theory. Tensors, as multidimensional arrays, find crucial applications in fields such as high-dimensional image analysis and hypergraph clustering. This paper explores the Farkas lemma within the context of tensor structures, extending its application within tensor theoretical frameworks. By introducing the concept of non-empty closed convex sets and relevant knowledge, and utilizing the separation theorem of points and closed convex sets, resulting in the derivation of the Farkas lemma within tensor.