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On the stability of solutions for semi-infinite vector optimization problems

Author

Listed:
  • Zai-Yun Peng

    (Chongqing JiaoTong University)

  • Jian-Wen Peng

    (Chongqing Normal University)

  • Xian-Jun Long

    (Chongqing Technology and Business University)

  • Jen-Chih Yao

    (China Medical University)

Abstract

This paper is concerned with the stability of semi-infinite vector optimization problems (SVO). Under weak assumptions, we establish sufficient conditions of the Berge-lower semicontinuity and lower Painlev $$\acute{e}$$ e ´ –Kuratowski convergence of weak efficient solutions for (SVO) under functional perturbations of both objective functions and constraint sets. Some examples are given to illustrate that our results are new and interesting.

Suggested Citation

  • Zai-Yun Peng & Jian-Wen Peng & Xian-Jun Long & Jen-Chih Yao, 2018. "On the stability of solutions for semi-infinite vector optimization problems," Journal of Global Optimization, Springer, vol. 70(1), pages 55-69, January.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:1:d:10.1007_s10898-017-0553-6
    DOI: 10.1007/s10898-017-0553-6
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    References listed on IDEAS

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    1. Todorov, Maxim Ivanov, 1996. "Kuratowski convergence of the efficient sets in the parametric linear vector semi-infinite optimization," European Journal of Operational Research, Elsevier, vol. 94(3), pages 610-617, November.
    2. N. Q. Huy & J.-C. Yao, 2011. "Semi-Infinite Optimization under Convex Function Perturbations: Lipschitz Stability," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 237-256, February.
    3. S. H. Hou & X. H. Gong & X. M. Yang, 2010. "Existence and Stability of Solutions for Generalized Ky Fan Inequality Problems with Trifunctions," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 387-398, August.
    4. S. Mishra & M. Jaiswal & H. Le Thi, 2012. "Nonsmooth semi-infinite programming problem using Limiting subdifferentials," Journal of Global Optimization, Springer, vol. 53(2), pages 285-296, June.
    5. T. Chuong & N. Huy & J. Yao, 2009. "Stability of semi-infinite vector optimization problems under functional perturbations," Computational Optimization and Applications, Springer, vol. 45(4), pages 583-595, December.
    6. Z. Y. Peng & X. M. Yang & J. W. Peng, 2012. "On the Lower Semicontinuity of the Solution Mappings to Parametric Weak Generalized Ky Fan Inequality," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 256-264, January.
    7. Chuong, T.D. & Huy, N.Q. & Yao, J.C., 2010. "Pseudo-Lipschitz property of linear semi-infinite vector optimization problems," European Journal of Operational Research, Elsevier, vol. 200(3), pages 639-644, February.
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    Cited by:

    1. Shiva Kapoor & C. S. Lalitha, 2021. "Essential stability in unified vector optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 161-175, May.
    2. Shiva Kapoor & C. S. Lalitha, 2019. "Stability in unified semi-infinite vector optimization," Journal of Global Optimization, Springer, vol. 74(2), pages 383-399, June.
    3. Xiangkai Sun & Kok Lay Teo & Xian-Jun Long, 2021. "Some Characterizations of Approximate Solutions for Robust Semi-infinite Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 281-310, October.

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