实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
AI总结：
本文基于增广对偶锥和Bishop-Phelps型分离函数，在实拓扑线性空间中推导出针对两个非凸锥的非线性锥分离新定理，其证明以凸集经典分离定理为关键工具。
摘要：
两个集合（或更具体地，两个锥）的分离在变分分析、凸分析、凸几何和优化等数学不同领域中发挥着重要作用。在本文中，我们推导了一些新结果，用于在实（拓扑）线性空间中通过（凸）锥/锥面分离两个非 necessarily 凸的锥。基本上，我们遵循 Kasimbeyli（2010, SIAM J. Optim. 20）提出的分离方法，该方法基于增广对偶锥和 Bishop-Phelps 型（范数线性）分离函数。凸集的经典分离定理是证明我们主要非线性锥分离定理的关键工具。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
