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Nonlinear Strict Cone Separation Theorems in Real Normed Spaces - MaRDI portal

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Nonlinear Strict Cone Separation Theorems in Real Normed Spaces

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Publication:6509148

arXiv2303.06392MaRDI QIDQ6509148

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Abstract: 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 Banach spaces. In essence, we follow the 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, in particular with respect to the cones involved. Moreover, in our results a certain novel subset of the augmented dual cone plays an important role.





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