In this paper we study a set optimization problem (SOP), i.e. we minimize a set-valued objective map F, which takes values on a real linear space Y equipped with a pre-order induced by a convex cone K. We introduce new order relations on the power set \documentclass[12pt]{minimal}
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\begin{document}$\mathcal{P}(Y)$\end{document} of Y (or on a subset of it), which are more suitable from a practical point of view than the often used minimizers in set optimization. Next, we propose a simple two-steps unifying approach to studying (SOP) w.r.t. various order relations. Firstly, we extend in a unified scheme some basic concepts of vector optimization, which are defined on the space Y up to an arbitrary nonempty pre-ordered set \documentclass[12pt]{minimal}
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\begin{document}$(\mathcal{Q},\preccurlyeq)$\end{document} without any topological or linear structure. Namely, we define the following concepts w.r.t. the pre-order \documentclass[12pt]{minimal}
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\begin{document}$\preccurlyeq$\end{document}: minimal elements, semicompactness, completeness, domination property of a subset of \documentclass[12pt]{minimal}
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\begin{document}$\mathcal{Q}$\end{document}, and semicontinuity of a set-valued map with values in \documentclass[12pt]{minimal}
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\begin{document}$\mathcal{Q}$\end{document} in a topological setting. Secondly, we establish existence results for optimal solutions of (SOP), when F takes values on \documentclass[12pt]{minimal}
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\begin{document}$(\mathcal{Q},\preccurlyeq)$\end{document} from which one can easily derive similar results for the case, when F takes values on \documentclass[12pt]{minimal}
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\begin{document}$\mathcal{P}(Y)$\end{document} equipped with various order relations.
