论文标题
Fenchel-moreau身份
Fenchel-Moreau identities on convex cones
论文作者
论文摘要
一个尖的凸锥自然会引起部分秩序，进一步的功能概念。我们考虑锥体上定义的扩展实用值的扩展功能。这些功能的单调共轭物可以与标准凸共轭物的类似方式定义。唯一的区别是，上皮是在锥体上而不是整个空间所取的。我们为锥体提供了足够的条件，相应的Fenchel-moreau双缀合同具有适当的，凸，较低的半连续和非稳定功能，并在锥体上定义了非稳定功能。此外，我们表明这些条件被称为完美锥体的一类锥体满足。
A pointed convex cone naturally induces a partial order, and further a notion of nondecreasingness for functions. We consider extended real-valued functions defined on the cone. Monotone conjugates for these functions can be defined in an analogous way to the standard convex conjugate. The only difference is that the supremum is taken over the cone instead of the entire space. We give sufficient conditions for the cone under which the corresponding Fenchel-Moreau biconjugation identity holds for proper, convex, lower semicontinuous, and nondecreasing functions defined on the cone. In addition, we show that these conditions are satisfied by a class of cones known as perfect cones.
