Abstract
In this paper, we introduce a construction method of total ordering cone on \({\mathbb{R}^n}\) . It is shown that any total ordering cone on \({\mathbb{R}^n}\) is isomorphic to the cone \({\mathbb{R}^n_{lex}}\) . Existence of a total ordering cone that contain given cone with a compact base is shown. By using this cone, a solving method of vector and set valued optimization problems is presented.
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Küçük, M., Soyertem, M. & Küçük, Y. On constructing total orders and solving vector optimization problems with total orders. J Glob Optim 50, 235–247 (2011). https://doi.org/10.1007/s10898-010-9576-y
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DOI: https://doi.org/10.1007/s10898-010-9576-y