Journal of Global Optimization

, Volume 59, Issue 4, pp 811-836

First online:

Benson type algorithms for linear vector optimization and applications

  • Andreas H. HamelAffiliated withYeshiva University
  • , Andreas LöhneAffiliated with Email author 
  • , Birgit RudloffAffiliated withPrinceton University

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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 set-valued risk measure for multivariate positions.


Vector optimization Multiple objective optimization Linear programming Duality Algorithms Outer approximation Set-valued risk measure Transaction costs

Mathematics Subject Classification

90C29 90C05 90-08 91G99