Abstract
An existence theorem of maximum points for a set preordered (not necessarily partial ordered) by a convex cone of a real linear space is presented. The proof of the theorem is different from the usual technic, that is the separation theorem, as used in Khazayel and Farajzadeh (Optim Lett 15:847–858, 2021) and Araya (Appl Math Lett 22:501–504, 2009). The main result of this gives an affirmative answer to the open problem was raised by Corley (J Optim Theory Appl 31(2):277–281, 1980) and also this paper can be viewed as a new version of the main theorem appeared in the above papers with mild assumptions and without using the separation theory and the notions of the topological interior or algebraic.
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Farajzadeh, A. On maximal and minimal elements for sets with respect to cones. Optim Lett (2023). https://doi.org/10.1007/s11590-023-02065-x
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DOI: https://doi.org/10.1007/s11590-023-02065-x