Journal of Global Optimization

, Volume 59, Issue 4, pp 811–836

Benson type algorithms for linear vector optimization and applications

  • Andreas H. Hamel
  • Andreas Löhne
  • Birgit Rudloff

DOI: 10.1007/s10898-013-0098-2

Cite this article as:
Hamel, A.H., Löhne, A. & Rudloff, B. J Glob Optim (2014) 59: 811. doi:10.1007/s10898-013-0098-2


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 set-valued risk measure for multivariate positions.


Vector optimizationMultiple objective optimization Linear programmingDualityAlgorithmsOuter approximationSet-valued risk measureTransaction costs

Mathematics Subject Classification


Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Andreas H. Hamel
    • 1
  • Andreas Löhne
    • 2
  • Birgit Rudloff
    • 3
  1. 1.Yeshiva UniversityNew YorkUSA
  2. 2.Martin-Luther-Universität Halle-WittenbergGermany
  3. 3.Princeton UniversityPrincetonUSA