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Aubin property for solution set in multi-objective programming

Author

Listed:
  • Morteza Rahimi

    (University of Tehran
    Kharazmi University)

  • Majid Soleimani-damaneh

    (University of Tehran)

Abstract

In this paper, the behavior of the solutions of a multi-objective optimization problem, whose the objective functions are perturbed by adding a small linear term, is analyzed. In this regard, a new notion of Lipschitzian stability, by means of the Aubin property of the solution set, is defined. Lipschitz stable locally efficient solutions, as generalization of tilt/full stable solutions, are introduced and characterized by modern variational analysis tools. Applying the weighted sum method, the relationships between these solutions and full-stable local optimal solutions of the scalarized problem are investigated. The key tools in deriving our results come from the first- and second-order variational analysis.

Suggested Citation

  • Morteza Rahimi & Majid Soleimani-damaneh, 2023. "Aubin property for solution set in multi-objective programming," Journal of Global Optimization, Springer, vol. 85(2), pages 441-460, February.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:2:d:10.1007_s10898-022-01209-0
    DOI: 10.1007/s10898-022-01209-0
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    References listed on IDEAS

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    1. Georgiev, Pando Gr. & Luc, Dinh The & Pardalos, Panos M., 2013. "Robust aspects of solutions in deterministic multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 229(1), pages 29-36.
    2. Sanaz Sadeghi & S. Morteza Mirdehghan, 2018. "Stability of Local Efficiency in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 591-613, August.
    3. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
    4. Ehrgott, Matthias & Ide, Jonas & Schöbel, Anita, 2014. "Minmax robustness for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 239(1), pages 17-31.
    5. Morteza Rahimi & Majid Soleimani-damaneh, 2018. "Robustness in Deterministic Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 137-162, October.
    6. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, December.
    7. Morteza Rahimi & Majid Soleimani-damaneh, 2020. "Characterization of Norm-Based Robust Solutions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 554-573, May.
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