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'''Benson's algorithm''', named after [[Harold Benson]], is a method for solving [[multi-objective linear programming
== Idea of algorithm ==
:<math>\
for
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]]).
== References ==▼
{{Reflist}}▼
== Dual algorithm ==
There is a dual variant of Benson's algorithm,<ref name="EhrgottLöhne2011">{{cite journal|last1=Ehrgott|first1=Matthias|last2=Löhne|first2=Andreas|last3=Shao|first3=Lizhen|title=A dual variant of Benson's "outer approximation algorithm" for multiple objective linear programming|journal=Journal of Global Optimization|volume=52|issue=4|year=2011|pages=757–778|issn=0925-5001|doi=10.1007/s10898-011-9709-y}}</ref> which is based on geometric duality<ref name="HeydeLöhne2008">{{cite journal|last1=Heyde|first1=Frank|last2=Löhne|first2=Andreas|title=Geometric Duality in Multiple Objective Linear Programming|journal=SIAM Journal on Optimization|volume=19|issue=2|year=2008|pages=836–845|issn=1052-6234|doi=10.1137/060674831|url=http://webdoc.sub.gwdg.de/ebook/serien/e/reports_Halle-Wittenberg_math/06-15report.pdf}}</ref> for multi-objective linear programs.
== Implementations ==
{{applied-math-stub}}▼
Bensolve - a free VLP solver
* [http://bensolve.org www.bensolve.org]
Inner
* [https://github.com/lcsirmaz/inner Link to github]
▲== References ==
▲{{Reflist}}
[[Category:Linear programming]]
[[Category:Optimization algorithms and methods]]
▲{{applied-math-stub}}
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