Journal of Global Optimization

, Volume 60, Issue 4, pp 713-736

First online:

Primal and dual approximation algorithms for convex vector optimization problems

  • Andreas LöhneAffiliated withDepartment of Mathematics, Martin-Luther-Universität Halle-Wittenberg
  • , Birgit RudloffAffiliated withDepartment of Operations Research and Financial Engineering, Princeton UniversityBendheim Center for Finance, Princeton University Email author 
  • , Firdevs UlusAffiliated withDepartment of Operations Research and Financial Engineering, Princeton University

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Two approximation algorithms for solving convex vector optimization problems (CVOPs) are provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously. The first algorithm is an extension of Benson’s outer approximation algorithm, and the second one is a dual variant of it. Both algorithms provide an inner as well as an outer approximation of the (upper and lower) images. Only one scalar convex program has to be solved in each iteration. We allow objective and constraint functions that are not necessarily differentiable, allow solid pointed polyhedral ordering cones, and relate the approximations to an appropriate \(\epsilon \)-solution concept. Numerical examples are provided.


Vector optimization Multiple objective optimization Convex programming Duality Algorithms Outer approximation