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An approximation algorithm for convex multi-objective programming problems

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  • Matthias Ehrgott

  • Lizhen Shao

  • Anita Schöbel

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  • Matthias Ehrgott & Lizhen Shao & Anita Schöbel, 2011. "An approximation algorithm for convex multi-objective programming problems," Journal of Global Optimization, Springer, vol. 50(3), pages 397-416, July.
    • Handle: RePEc:spr:jglopt:v:50:y:2011:i:3:p:397-416
    DOI: 10.1007/s10898-010-9588-7
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    References listed on IDEAS

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    1. Lizhen Shao & Matthias Ehrgott, 2008. "Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(2), pages 257-276, October.
    2. Miettinen, Kaisa & Makela, Marko M. & Kaario, Katja, 2006. "Experiments with classification-based scalarizing functions in interactive multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 175(2), pages 931-947, December.
    3. H. P. Benson, 1998. "Hybrid Approach for Solving Multiple-Objective Linear Programs in Outcome Space," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 17-35, July.
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    Cited by:

    1. Andreas Löhne & Birgit Rudloff & Firdevs Ulus, 2014. "Primal and dual approximation algorithms for convex vector optimization problems," Journal of Global Optimization, Springer, vol. 60(4), pages 713-736, December.
    2. Rasmus Bokrantz & Anders Forsgren, 2013. "An Algorithm for Approximating Convex Pareto Surfaces Based on Dual Techniques," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 377-393, May.
    3. Timothy C. Y. Chan & Tim Craig & Taewoo Lee & Michael B. Sharpe, 2014. "Generalized Inverse Multiobjective Optimization with Application to Cancer Therapy," Operations Research, INFORMS, vol. 62(3), pages 680-695, June.
    4. Gabriele Eichfelder & Julia Niebling & Stefan Rocktäschel, 2020. "An algorithmic approach to multiobjective optimization with decision uncertainty," Journal of Global Optimization, Springer, vol. 77(1), pages 3-25, May.
    5. Daniel Dörfler, 2022. "On the Approximation of Unbounded Convex Sets by Polyhedra," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 265-287, July.
    6. Wei-tian Wu & Xin-min Yang, 2024. "Reference-point-based branch and bound algorithm for multiobjective optimization," Journal of Global Optimization, Springer, vol. 88(4), pages 927-945, April.
    7. Lizhen Shao & Matthias Ehrgott, 2014. "An objective space cut and bound algorithm for convex multiplicative programmes," Journal of Global Optimization, Springer, vol. 58(4), pages 711-728, April.
    8. Lamia Zerfa & Mohamed El-Amine Chergui, 2022. "Finding non dominated points for multiobjective integer convex programs with linear constraints," Journal of Global Optimization, Springer, vol. 84(1), pages 95-117, September.
    9. Andreas Hamel & Andreas Löhne & Birgit Rudloff, 2014. "Benson type algorithms for linear vector optimization and applications," Journal of Global Optimization, Springer, vol. 59(4), pages 811-836, August.
    10. Gabriela Kováčová & Birgit Rudloff, 2022. "Convex projection and convex multi-objective optimization," Journal of Global Optimization, Springer, vol. 83(2), pages 301-327, June.
    11. Zachary Feinstein & Birgit Rudloff, 2024. "Deep learning the efficient frontier of convex vector optimization problems," Journal of Global Optimization, Springer, vol. 90(2), pages 429-458, October.
    12. Çağın Ararat & Firdevs Ulus & Muhammad Umer, 2022. "A Norm Minimization-Based Convex Vector Optimization Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 681-712, August.
    13. Koenen, Melissa & Balvert, Marleen & Fleuren, H.A., 2023. "A Renewed Take on Weighted Sum in Sandwich Algorithms : Modification of the Criterion Space," Discussion Paper 2023-012, Tilburg University, Center for Economic Research.
    14. Cacchiani, Valentina & D’Ambrosio, Claudia, 2017. "A branch-and-bound based heuristic algorithm for convex multi-objective MINLPs," European Journal of Operational Research, Elsevier, vol. 260(3), pages 920-933.
    15. Birgit Rudloff & Firdevs Ulus, 2019. "Certainty Equivalent and Utility Indifference Pricing for Incomplete Preferences via Convex Vector Optimization," Papers 1904.09456, arXiv.org, revised Oct 2020.
    16. Zachary Feinstein & Birgit Rudloff, 2017. "A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle," Journal of Global Optimization, Springer, vol. 68(1), pages 47-69, May.
    17. Zachary Feinstein & Birgit Rudloff, 2015. "A recursive algorithm for multivariate risk measures and a set-valued Bellman's principle," Papers 1508.02367, arXiv.org, revised Jul 2016.
    18. Koenen, Melissa & Balvert, Marleen & Fleuren, H.A., 2023. "A Renewed Take on Weighted Sum in Sandwich Algorithms : Modification of the Criterion Space," Other publications TiSEM 795b6c0c-c7bc-4ced-9d6b-a, Tilburg University, School of Economics and Management.
    19. Ina Lammel & Karl-Heinz Küfer & Philipp Süss, 2025. "Efficient Approximation Quality Computation for Sandwiching Algorithms for Convex Multicriteria Optimization," Journal of Optimization Theory and Applications, Springer, vol. 204(3), pages 1-21, March.
    20. Zachary Feinstein & Birgit Rudloff, 2022. "Deep Learning the Efficient Frontier of Convex Vector Optimization Problems," Papers 2205.07077, arXiv.org, revised May 2024.
    21. Gabriele Eichfelder & Kathrin Klamroth & Julia Niebling, 2021. "Nonconvex constrained optimization by a filtering branch and bound," Journal of Global Optimization, Springer, vol. 80(1), pages 31-61, May.
    22. Bazgan, Cristina & Jamain, Florian & Vanderpooten, Daniel, 2017. "Discrete representation of the non-dominated set for multi-objective optimization problems using kernels," European Journal of Operational Research, Elsevier, vol. 260(3), pages 814-827.
    23. Firdevs Ulus, 2018. "Tractability of convex vector optimization problems in the sense of polyhedral approximations," Journal of Global Optimization, Springer, vol. 72(4), pages 731-742, December.
    24. Raimundo, Marcos M. & Ferreira, Paulo A.V. & Von Zuben, Fernando J., 2020. "An extension of the non-inferior set estimation algorithm for many objectives," European Journal of Operational Research, Elsevier, vol. 284(1), pages 53-66.
    25. Gabriela Kováčová & Firdevs Ulus, 2024. "Computing the recession cone of a convex upper image via convex projection," Journal of Global Optimization, Springer, vol. 89(4), pages 975-994, August.

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