Nonlinear strict cone separation theorems in real normed spaces

Research output: Contribution to journalArticleResearchpeer review

Authors

  • Christian Günther
  • Christiane Tammer
  • Bahareh Khazayel

Research Organisations

External Research Organisations

  • Martin Luther University Halle-Wittenberg
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Details

Original languageEnglish
Pages (from-to)601-623
Number of pages23
JournalJournal of Nonlinear and Variational Analysis
Volume8
Issue number4
Early online date1 May 2024
Publication statusPublished - 1 Aug 2024

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) 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-Castaño, Melguizo-Padial and Parzanese.

Keywords

    Augmented dual cone, Bishop-Phelps cone, Cone separation, Nonconvex cone, Separation theorem

ASJC Scopus subject areas

Cite this

Nonlinear strict cone separation theorems in real normed spaces. / Günther, Christian; Tammer, Christiane; Khazayel, Bahareh.
In: Journal of Nonlinear and Variational Analysis, Vol. 8, No. 4, 01.08.2024, p. 601-623.

Research output: Contribution to journalArticleResearchpeer review

Günther, C, Tammer, C & Khazayel, B 2024, 'Nonlinear strict cone separation theorems in real normed spaces', Journal of Nonlinear and Variational Analysis, vol. 8, no. 4, pp. 601-623. https://doi.org/10.48550/arXiv.2303.06392, https://doi.org/10.23952/jnva.8.2024.4.08
Günther, C., Tammer, C., & Khazayel, B. (2024). Nonlinear strict cone separation theorems in real normed spaces. Journal of Nonlinear and Variational Analysis, 8(4), 601-623. https://doi.org/10.48550/arXiv.2303.06392, https://doi.org/10.23952/jnva.8.2024.4.08
Günther C, Tammer C, Khazayel B. Nonlinear strict cone separation theorems in real normed spaces. Journal of Nonlinear and Variational Analysis. 2024 Aug 1;8(4):601-623. Epub 2024 May 1. doi: 10.48550/arXiv.2303.06392, 10.23952/jnva.8.2024.4.08
Günther, Christian ; Tammer, Christiane ; Khazayel, Bahareh. / Nonlinear strict cone separation theorems in real normed spaces. In: Journal of Nonlinear and Variational Analysis. 2024 ; Vol. 8, No. 4. pp. 601-623.
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