Nonlinear Strict Cone Separation Theorems in Real Normed Spaces
arxiv(2023)
摘要
In this paper, we derive some new results for the separation of two not
necessarily convex cones by a (convex) cone / conical surface in real
(reflexive) normed spaces. In essence, we follow the nonlinear and nonsymmetric
separation approach developed by Kasimbeyli (2010, SIAM J. Optim. 20), which is
based on augmented dual cones and Bishop-Phelps type (normlinear) separating
functions. Compared to Kasimbeyli's separation theorem, we formulate our
theorems for the separation of two cones under weaker conditions (concerning
convexity and closedness requirements) with respect to the involved cones. By a
new characterization of the algebraic interior of augmented dual cones in real
normed spaces, we are able to establish relationships between our cone
separation results and the results derived by Kasimbeyli (2010, SIAM J. Optim.
20) and by Garcia-Castano, Melguizo-Padial and Parzanese (2023, Math. Meth.
Oper. Res. 97).
更多查看译文
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要