论文标题
混合晶格结构和锥体预测
Mixed lattice structures and cone projections
论文作者
论文摘要
在优化理论和相关领域中经常遇到与封闭凸锥上预测有关的问题。为了研究这些问题，已经引入了各种统一的想法，包括不对称的矢量标准规范和某些普遍的晶格样操作。我们通过描述如何使用本文开发的订单理论形式主义来提出锥体投影问题，对这些研究提出了新的观点。基础数学结构是一个部分有序的向量空间，它通过使用两个部分订购来概括向量晶格的概念，并且相对于这些顺序具有某些晶格型属性。在本说明中，我们介绍了这些所谓的混合晶格空间的概括，并展示了上述某些应用中如何自然出现这种结构。
Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have been introduced, including asymmetric vector-valued norms and certain generalized lattice-like operations. We propose a new perspective on these studies by describing how the problem of cone projection can be formulated using an order-theoretic formalism developed in this paper. The underlying mathematical structure is a partially ordered vector space that generalizes the notion of a vector lattice by using two partial orderings and having certain lattice-type properties with respect to these orderings. In this note we introduce a generalization of these so-called mixed lattice spaces, and we show how such structures arise quite naturally in some of the applications mentioned above.
