---
abstract: ' is an open source implementation of Benson’s algorithm and its dual variant. Both algorithms compute primal and dual solutions of vector linear programs (VLP), which include the subclass of multiple objective linear programs (MOLP). The recent version of  can treat arbitrary vector linear programs whose upper image does not contain lines. This article surveys the theoretical background of the implementation. In particular, the role of VLP duality for the implementation is pointed out. Some numerical examples are provided. In contrast to the existing literature we consider a less restrictive class of vector linear programs.'
address:
- |
    Friedrich Schiller University Jena\
    Department of Mathematics\
    07737 Jena\
    Germany
- |
    Martin Luther University Halle–Wittenberg\
    Department of Mathematics\
    06099 Halle (Saale)\
    Germany
author:
- Andreas Löhne
- Benjamin Weißing
bibliography:
- 'database.bib'
title: 'The vector linear program solver [*Bensolve*]{} – notes on theoretical background'
---

vector linear programming ,linear vector optimization , multiple objective optimization 90C29 ,90C05 ,52B55 ,15A39

Introduction
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Solution concepts
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Dual problem and dual solutions
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A few remarks on the algorithms
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Numerical results
=================

Bibliography {#bibliography .unnumbered}
============
