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Consider a vector linear program
:<math>\min_C Px \; \text{ subject to } A x \geq b</math>
for <math>P \in \mathbb{R}^{q \times n}</math>, <math>A \in \mathbb{R}^{m \times n}</math>, <math>b \in \mathbb{R}^m</math> and a polyhedral convex ordering cone <math>C</math> having nonempty interior and containing no lines. The feasible set is <math>S=\{x \in \mathbb{R}^n:\; A x \geq b\}</math>. In particular, Benson's algorithm finds the [[extreme point]]s of the set <math>P[S] + C</math>, which is called upper image.<ref name="Lohne"/>
In case of <math>C=\mathbb{R}^q_+:=\{y \in \mathbb{R}^q : y_1 \geq 0,\dots, y_q \geq 0\}</math>, one obtains the special case of a multi-objective linear program ([[multiobjective optimization]]).
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