论文标题
实际拓扑线性空间中的非线性锥分离定理
Nonlinear Cone Separation Theorems in Real Topological Linear Spaces
论文作者
论文摘要
两组（或更具体的两个锥体）的分离在数学的不同领域（例如变分析，凸分析，凸几何，优化）中起重要作用。在本文中，我们得出了一些新的结果，以通过在实际（拓扑）线性空间中通过（凸）锥体表面分离两个凸锥。基本上，我们遵循Kasimbeyli（2010，Siam J.Optim。20）的分离方法，基于增强的双锥和Bishop-phelps类型（Normlinear）分离功能。凸集的经典分离定理是证明我们主要的非线性锥体分离定理的关键工具。
The separation of two sets (or more specific of two cones) plays an important role in different fields of mathematics such as variational analysis, convex analysis, convex geometry, optimization. In the paper, we derive some new results for the separation of two not necessarily convex cones by a (convex) cone / conical surface in real (topological) linear spaces. Basically, we follow the separation approach by Kasimbeyli (2010, SIAM J. Optim. 20) based on augmented dual cones and Bishop-Phelps type (normlinear) separating functions. Classical separation theorems for convex sets are the key tool for proving our main nonlinear cone separation theorems.
