Symmetric and Non-symmetric Cone Separation via Bishop-Phelps Cones in Normed Spaces

Fernando García-Castaño (), Christian Günther (), Miguel Ángel Melguizo-Padial () and Christiane Tammer ()
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Fernando García-Castaño: University of Alicante
Christian Günther: Institut für Angewandte Mathematik
Miguel Ángel Melguizo-Padial: University of Alicante
Christiane Tammer: Martin Luther University Halle-Wittenberg

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 3, No 29, 38 pages

Abstract: Abstract In this paper, we study relationships between symmetric and non-symmetric separation of (not necessarily convex) cones by using separating cones of Bishop-Phelps type in real normed spaces. Besides extending some known results for the non-symmetric cone separation approach, we propose a new symmetric cone separation approach and establish cone separation results for it by using some cone separation results obtained for the non-symmetric cone separation approach twice (by swapping the roles of the cones). In addition to specifically emphasizing the results for the convex case, we also present some existence results for (bounded) convex bases of convex cones. Finally, we highlight some applications of symmetric and non-symmetric cone separation in optimization.

Keywords: Symmetric cone separation; Non-symmetric cone separation; Nonconvex cone; Bishop-Phelps separating cone; Norm-linear separating function; 90C29; 90C25; 90C31; 90C48; 46N10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02836-9

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