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Cone Characterizations of Approximate Solutions in Real Vector Optimization

Author

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  • A. Engau

    (Clemson University)

  • M. M. Wiecek

    (Clemson University)

Abstract

Approximate nondominated solutions of real vector optimization problems are characterized using the concept of translated cones. Relationships between these solutions and Pareto nondominated points are examined, and the problem of optimizing over the set of approximate solutions is addressed.

Suggested Citation

  • A. Engau & M. M. Wiecek, 2007. "Cone Characterizations of Approximate Solutions in Real Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 499-513, September.
    • Handle: RePEc:spr:joptap:v:134:y:2007:i:3:d:10.1007_s10957-007-9235-8
    DOI: 10.1007/s10957-007-9235-8
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    References listed on IDEAS

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    1. A. Cambini & D.T. Luc & L. Martein, 2003. "Order-Preserving Transformations and Applications," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 275-293, August.
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    3. S. Ruzika & M. M. Wiecek, 2005. "Approximation Methods in Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 473-501, September.
    4. Engau, Alexander & Wiecek, Margaret M., 2007. "Generating [epsilon]-efficient solutions in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1566-1579, March.
    5. K. R. Kazmi, 2001. "Existence of ∈-Minima for Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 667-674, June.
    6. C. Gutiérrez & B. Jiménez & V. Novo, 2006. "On Approximate Efficiency in Multiobjective Programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 165-185, August.
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    Cited by:

    1. Thai Doan Chuong, 2022. "Approximate solutions in nonsmooth and nonconvex cone constrained vector optimization," Annals of Operations Research, Springer, vol. 311(2), pages 997-1015, April.
    2. M. Golestani & H. Sadeghi & Y. Tavan, 2018. "Nonsmooth Multiobjective Problems and Generalized Vector Variational Inequalities Using Quasi-Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 896-916, December.
    3. Stephan Dempe & Gabriele Eichfelder & Jörg Fliege, 2015. "On the effects of combining objectives in multi-objective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(1), pages 1-18, August.
    4. Daniel Vanderpooten & Lakmali Weerasena & Margaret M. Wiecek, 2017. "Covers and approximations in multiobjective optimization," Journal of Global Optimization, Springer, vol. 67(3), pages 601-619, March.
    5. Engau, Alexander, 2009. "Tradeoff-based decomposition and decision-making in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 199(3), pages 883-891, December.
    6. Arne Herzel & Stephan Helfrich & Stefan Ruzika & Clemens Thielen, 2023. "Approximating biobjective minimization problems using general ordering cones," Journal of Global Optimization, Springer, vol. 86(2), pages 393-415, June.

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