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Some Remarks on the Minty Vector Variational Inequality

Author

Listed:
  • X. M. Yang

    (Chongqing Normal University)

  • X. Q. Yang

    (Hong Kong Polytechnic University)

  • K. L. Teo

    (Hong Kong Polytechnic University)

Abstract

In this paper, we establish some relations between a Minty vector variational inequality and a vector optimization problem under pseudoconvexity or pseudomonotonicity, respectively. Our results generalize those of Ref. 1.

Suggested Citation

  • X. M. Yang & X. Q. Yang & K. L. Teo, 2004. "Some Remarks on the Minty Vector Variational Inequality," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 193-201, April.
    • Handle: RePEc:spr:joptap:v:121:y:2004:i:1:d:10.1023_b:jota.0000026137.18526.7a
    DOI: 10.1023/B:JOTA.0000026137.18526.7a
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    References listed on IDEAS

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    1. D.E. Ward & G.M. Lee, 2002. "On Relations Between Vector Optimization Problems and Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 583-596, June.
    2. X. Q. Yang & C. J. Goh, 1997. "On Vector Variational Inequalities: Application to Vector Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 95(2), pages 431-443, November.
    3. X. Q. Yang, 1997. "Vector Variational Inequality and Vector Pseudolinear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 729-734, December.
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    Citations

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    Cited by:

    1. Crespi Giovanni P. & Ginchev Ivan & Rocca Matteo, 2004. "Increase-along-rays property for vector functions," Economics and Quantitative Methods qf04015, Department of Economics, University of Insubria.
    2. Ya-Ping Fang & Rong Hu, 2007. "Estimates of approximate solutions and well-posedness for variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 281-291, April.
    3. Xiao-bo Li & Fu-quan Xia, 2013. "Hadamard well-posedness of a general mixed variational inequality in Banach space," Journal of Global Optimization, Springer, vol. 56(4), pages 1617-1629, August.
    4. Giovanni P. Crespi & Matteo Rocca & Carola Schrage, 2015. "Variational Inequalities Characterizing Weak Minimality in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 804-824, September.
    5. M. Oveisiha & J. Zafarani, 2012. "Vector optimization problem and generalized convexity," Journal of Global Optimization, Springer, vol. 52(1), pages 29-43, January.
    6. Qamrul Ansari & Mahboubeh Rezaie & Jafar Zafarani, 2012. "Generalized vector variational-like inequalities and vector optimization," Journal of Global Optimization, Springer, vol. 53(2), pages 271-284, June.
    7. Yong Zhao & Jin Zhang & Xinmin Yang & Gui-Hua Lin, 2017. "Expected Residual Minimization Formulation for a Class of Stochastic Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 545-566, November.
    8. Li, X.B. & Li, S.J., 2014. "Hölder continuity of perturbed solution set for convex optimization problems," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 908-918.
    9. Giovanni P. Crespi & Carola Schrage, 2021. "Applying set optimization to weak efficiency," Annals of Operations Research, Springer, vol. 296(1), pages 779-801, January.
    10. Ren-you Zhong & Nan-jing Huang, 2010. "Stability Analysis for Minty Mixed Variational Inequality in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 454-472, December.
    11. Q. H. Ansari & G. M. Lee, 2010. "Nonsmooth Vector Optimization Problems and Minty Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 1-16, April.
    12. S. Al-Homidan & Q. H. Ansari, 2010. "Generalized Minty Vector Variational-Like Inequalities and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 1-11, January.
    13. Syed Shakaib Irfan & Mijanur Rahaman & Iqbal Ahmad & Rais Ahmad & Saddam Husain, 2019. "Generalized Nonsmooth Exponential-Type Vector Variational-Like Inequalities and Nonsmooth Vector Optimization Problems in Asplund Spaces," Mathematics, MDPI, vol. 7(4), pages 1-11, April.

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