论文标题
找到一组分段仿射功能的全局最小化器
Finding the set of global minimizers of a piecewise affine function
论文作者
论文摘要
在目前的工作中，我们研究了找到分段仿射功能的全球最小值的问题。我们在Coexhauster方面为问题采用最佳条件，并使用它们来陈述并证明从下方界定分段仿射功能的必要条件。我们基于这些条件构建一种简单的方法，该方法允许人们获得研究功能的最小值以及其所有全局最小化器的相应集。这些结果是通过Coexhauster概念构建的。这个概念是由V. F. Demyanov引入的。 Coexhausters是凸紧凑型集合的家族，允许一个人以仿射函数的minmax或maxmin的形式表示所研究函数的增量的近似。我们以这些表示形式为定义，并表明它们与其他研究人员给出的分段仿射功能的定义相对应。所有条件和方法都是通过Coexhausters理论获得的。在本文中，我们从该理论中给出了一些必要的事实。在整个论文中提供了许多说明性的数字示例。
In the present work we study a problem of finding a global minimum of a piecewise affine function. We employ optimality conditions for the problem in terms of coexhausters and use them to state and prove necessary and sufficient conditions for a piecewise affine function to be bounded from below. We construct a simple method based on these conditions which allows one to get the minimum value of a studied function and the corresponding set of all its global minimizers. These results are built via coexhauster notion. This notion was introduced by V. F. Demyanov. Coexhausters are families of convex compact sets that allow one to represent the approximation of the increment of the studied function at a considered point in the form of minmax or maxmin of affine functions. We take these representations as a definition of a piecewise affine function and show that they correspond with the definitions for piecewise affine function given by other researchers. All the conditions and methods were obtained by means of coexhausters theory. In the paper we give some necessary facts from this theory. A lot of illustrative numerical examples are provided throughout the paper.
