Benson's algorithm

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Benson's algorithm, named after Harold Benson, is a method for solving linear multi-objective optimization problems. This works by finding the "efficient extreme points in the outcome set".^[1] The primary concept in Benson's algorithm is to evaluate the upper image of the vector optimization problem by cutting planes.^[2]

Idea of algorithm

Given a linear vector optimization problem

\min Px\;{\text{ subject to }}x\in S

for some $P\in \mathbb {R} ^{m\times n}$ and a nonempty polyhedron $S\subset \mathbb {R} ^{n}$ , then Benson's algorithm will find the extreme points of the set $P[S]+\mathbb {R} _{+}^{m}$ .^[2]

References

^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1023/A:1008215702611, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1023/A:1008215702611 instead.
^ ^a ^b Andreas Löhne (2011). Vector Optimization with Infimum and Supremum. Springer. pp. 162–169. ISBN 9783642183508.

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[Benson-1] Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1023/A:1008215702611, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1023/A:1008215702611 instead.

[Lohne-2] Andreas Löhne (2011). Vector Optimization with Infimum and Supremum. Springer. pp. 162–169. ISBN 9783642183508.

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