局部凸空间中的集合极小元的刻画

Efficient Solution of Set Describe in Local Convex Space

在局部凸空间下,将一般对偶锥推广,引入了扩展对偶锥,用其中的元素定义了一类单调增的次线性函数.给出了扩展对偶锥的一些性质,利用对非凸向量优化问题的简单有效的纯量技巧,证明集合的有效点解可以通过计算某个次线性泛函的最小点得到.

In this paper, in local convex spaces by extending a usual definition of dual cones , an augmented dual of a cone is introduced. A special class of monotonically increasing sub - linear function are defined by using the elements of the augmented dual cone . As an application, a simple and efficient scalafization technique is shown that any properly minimal point of a set in local convex space can be calculated by miniminizing a certain sublinear functional.