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Image Space Analysis for Constrained Inverse Vector Variational Inequalities via Multiobjective Optimization

Author

Listed:
  • Jiawei Chen

    (Southwest University)

  • Elisabeth Köbis

    (Martin Luther University Halle-Wittenberg, Institute of Mathematics)

  • Markus Köbis

    (Freie universität Berlin)

  • Jen-Chih Yao

    (China Medical University
    King Abdulaziz University)

Abstract

In this paper, we employ the image space analysis to study constrained inverse vector variational inequalities. First, sufficient and necessary optimality conditions for constrained inverse vector variational inequalities are established by using multiobjective optimization. A continuous nonlinear function is also introduced based on the oriented distance function and projection operator. This function is proven to be a weak separation function and a regular weak separation function under different parameter sets. Then, two alternative theorems are established, which lead directly to sufficient and necessary optimality conditions of the inverse vector variational inequalities. This provides a partial answer to an open question posed in Chen et al. (J Optim Theory Appl 166:460–479, 2015).

Suggested Citation

  • Jiawei Chen & Elisabeth Köbis & Markus Köbis & Jen-Chih Yao, 2018. "Image Space Analysis for Constrained Inverse Vector Variational Inequalities via Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 816-834, June.
    • Handle: RePEc:spr:joptap:v:177:y:2018:i:3:d:10.1007_s10957-017-1197-x
    DOI: 10.1007/s10957-017-1197-x
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    References listed on IDEAS

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    1. Reinhard John, 2007. "Local and Global Consumer Preferences," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 315-325, Springer.
    2. Jiawei Chen & Shengjie Li & Zhongping Wan & Jen-Chih Yao, 2015. "Vector Variational-Like Inequalities with Constraints: Separation and Alternative," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 460-479, August.
    3. S. J. Li & Y. D. Xu & S. K. Zhu, 2012. "Nonlinear Separation Approach to Constrained Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 842-856, September.
    4. He, Bingsheng & He, Xiao-Zheng & Liu, Henry X., 2010. "Solving a class of constrained 'black-box' inverse variational inequalities," European Journal of Operational Research, Elsevier, vol. 204(3), pages 391-401, August.
    5. J. B. Hiriart-Urruty, 1979. "Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 79-97, February.
    6. Marius Durea & Radu Strugariu & Christiane Tammer, 2015. "On set-valued optimization problems with variable ordering structure," Journal of Global Optimization, Springer, vol. 61(4), pages 745-767, April.
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    Cited by:

    1. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2020. "Robustness Characterizations for Uncertain Optimization Problems via Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 459-479, August.
    2. Qamrul Hasan Ansari & Elisabeth Köbis & Pradeep Kumar Sharma, 2019. "Characterizations of Multiobjective Robustness via Oriented Distance Function and Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 817-839, June.
    3. Elisabeth Köbis & Markus A. Köbis & Xiaolong Qin, 2019. "Nonlinear Separation Approach to Inverse Variational Inequalities in Real Linear Spaces," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 105-121, October.

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