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24 Aug 2013
Benson type algorithms for linear vector optimization and applications
 Andreas H. Hamel,
 Andreas Löhne,
 Birgit Rudloff
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New versions and extensions of Benson’s outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each iteration rather than two or three as in previous versions. Extensions are given to problems with arbitrary pointed solid polyhedral ordering cones. Numerical examples are provided, one of them involving a new setvalued risk measure for multivariate positions.
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 Title
 Benson type algorithms for linear vector optimization and applications
 Journal

Journal of Global Optimization
Volume 59, Issue 4 , pp 811836
 Cover Date
 20140801
 DOI
 10.1007/s1089801300982
 Print ISSN
 09255001
 Online ISSN
 15732916
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Vector optimization
 Multiple objective optimization
 Linear programming
 Duality
 Algorithms
 Outer approximation
 Setvalued risk measure
 Transaction costs
 90C29
 90C05
 9008
 91G99
 Industry Sectors
 Authors

 Andreas H. Hamel ^{(1)}
 Andreas Löhne ^{(2)}
 Birgit Rudloff ^{(3)}
 Author Affiliations

 1. Yeshiva University, New York, USA
 2. MartinLutherUniversität HalleWittenberg, Germany
 3. Princeton University, Princeton, USA