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Approximations of unbounded convex projections and unbounded convex sets

Author

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  • Gabriela Kováčová

    (University of California, Los Angeles)

  • Birgit Rudloff

    (Vienna University of Economics and Business)

Abstract

We consider the problem of projecting a convex set onto a subspace or, equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex sets by polyhedrons. The existing literature on convex projections provides methods for bounded convex sets only, in this paper we propose a method that can handle both bounded and unbounded problems. The algorithms we propose build on the ideas of inner and outer approximation. In particular, we adapt the recently proposed methods for solving unbounded convex vector optimization problems to handle also the class of projection problems.

Suggested Citation

  • Gabriela Kováčová & Birgit Rudloff, 2025. "Approximations of unbounded convex projections and unbounded convex sets," Journal of Global Optimization, Springer, vol. 91(4), pages 787-805, April.
    • Handle: RePEc:spr:jglopt:v:91:y:2025:i:4:d:10.1007_s10898-024-01461-6
    DOI: 10.1007/s10898-024-01461-6
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    References listed on IDEAS

    as
    1. Gabriela Kováčová & Birgit Rudloff, 2022. "Convex projection and convex multi-objective optimization," Journal of Global Optimization, Springer, vol. 83(2), pages 301-327, June.
    2. 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.
    3. Gabriela Kováčová & Birgit Rudloff, 2021. "Time Consistency of the Mean-Risk Problem," Operations Research, INFORMS, vol. 69(4), pages 1100-1117, July.
    4. Zachary Feinstein & Birgit Rudloff & Jianfeng Zhang, 2022. "Dynamic Set Values for Nonzero-Sum Games with Multiple Equilibriums," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 616-642, February.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

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