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In this paper, vector optimization is considered in the framework of decisionmaking and optimization in general spaces. Interdependencies between dominationstructures in decision making and domination sets in vector optimization aregiven. We prove some basic properties of efficient and of weakly efficientpoints in vector optimization. Sufficient conditions for solutions to vectoroptimization problems are shown using minimal solutions of functionals. Wefocus on the scalarization by functions with uniform sublevel sets, which alsodelivers necessary conditions for efficiency and weak efficiency. The functionswith uniform sublevel sets may be, e.g., continuous or even Lipschitzcontinuous, convex, strictly quasiconcave or sublinear. They can coincide withan order unit norm on a subset of the space.

Scalarization in vector optimization by functions with uniform sublevel sets