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Path connectedness of the efficient solution set for generalized vector quasi-equilibrium problems

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Abstract

In this paper, the efficient solution set for generalized vector quasi-equilibrium problems is investigated. By means of the linear scalarization method, we establish the path connectedness of the efficient solution set for generalized vector quasi-equilibrium problems under some suitable conditions.

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References

  1. Ansari, Q.H., Flores-Bazán, F.: Generalized vector quasi-equilibrium problems with applications. J. Math. Anal. Appl. 277, 246–256 (2003)

    Article  MathSciNet  Google Scholar 

  2. Ansari, Q.H., Köbis, E., Sharma, P.K.: Characterizations of set relations with respect to variable domination structures via oriented distance function. Optimization 67, 1389–1407 (2018)

    Article  MathSciNet  Google Scholar 

  3. Ansari, Q.H., Köbis, E., Sharma, P.K.: Characterizations of multiobjective robustness via oriented distance function and image space analysis. J. Optim. Theory Appl. 181, 817–839 (2019)

    Article  MathSciNet  Google Scholar 

  4. Ansari, Q.H., Hamel, A.H., Sharma, P.K.: Ekeland’s variational principle with weighted set order relations. Math. Methods Oper. Res. 91, 117–136 (2020)

    Article  MathSciNet  Google Scholar 

  5. Ansari, Q.H., Sharma, P.K., Qin, X.: Characterizations of robust optimality conditions via image space analysis. Optimization 69, 2063–2083 (2020)

    Article  MathSciNet  Google Scholar 

  6. Lee, G.M., Kim, D.S., Lee, B.S., Yen, N.D.: Vector variational inequality as a tool for studying vector optimization problems. Nonlinear Anal. 34, 745–765 (1998)

    Article  MathSciNet  Google Scholar 

  7. Cheng, Y.H.: On the connectedness of the solution set for the weak vector variational inequality. J. Math. Anal. Appl. 260, 1–5 (2001)

    Article  MathSciNet  Google Scholar 

  8. Gong, X.H.: Efficiency and henig efficiency for vector equilibrium problems. J. Optim. Theory Appl. 108, 139–154 (2001)

    Article  MathSciNet  Google Scholar 

  9. Liu, Q.Y., Long, X.J., Huang, N.J.: Connectedness of the sets of weak efficient solutions for generalized vector equilibrium problems. Math. Slovaca 62, 123–136 (2012)

    Article  MathSciNet  Google Scholar 

  10. Gong, X.H.: Connectedness of the solution sets and scalarization for vector equilibrium problems. J. Optim. Theory Appl. 133, 151–161 (2007)

    Article  MathSciNet  Google Scholar 

  11. Gong, X.H., Yao, J.C.: Connectedness of the set of efficient solutions for generalized systems. J. Optim. Theory Appl. 138, 189–196 (2008)

    Article  MathSciNet  Google Scholar 

  12. Han, Y., Huang, N.J.: The connectedness of the solutions set for generalized vector equilibrium problems. Optimization 65, 357–367 (2016)

    Article  MathSciNet  Google Scholar 

  13. Xu, Y.D., Zhang, P.P.: Connectedness of solution sets of strong vector equilibrium problems with an application. J. Optim. Theory Appl. 178, 131–152 (2018)

    Article  MathSciNet  Google Scholar 

  14. Han, Y., Huang, N.J.: Existence and connectedness of solutions for generalized vector quasi-equilibrium problems. J. Optim. Theory Appl. 179, 65–85 (2018)

    Article  MathSciNet  Google Scholar 

  15. Gong, X.H.: On the contractibility and connectedness of an efficient point set. J. Math. Anal. Appl. 264, 465–478 (2001)

    Article  MathSciNet  Google Scholar 

  16. Jahn, J.: Vector Optimization: Theory, Applications, and Extensions. Springer, Berlin (2011)

    Book  Google Scholar 

  17. Peng, Z.Y., Zhao, Y., Yang, X.M.: Semicontinuity of approximate solution mappings to parametric set-valued weak vector equilibrium problems. Numer. Funct. Anal. Optim. 36, 481–500 (2015)

    Article  MathSciNet  Google Scholar 

  18. Han, Y., Huang, N.J.: Existence and stability of solutions for a class of generalized vector equilibrium problems. Positivity 20, 829–846 (2016)

    Article  MathSciNet  Google Scholar 

  19. Giannessi, F. (ed.): Vector Variational Inequalities and Vector Equilibria: Mathematical Theories. Kluwer Academic Publishers, Dordrecht (2000)

    MATH  Google Scholar 

  20. Aubin, J.P., Ekeland, I.: Applied Nonlinear Analysis. Wiley, New York (1984)

    MATH  Google Scholar 

  21. Göpfert, A., Riahi, H., Tammer, C., Zǎlinescu, C.: Variational Methods in Partially Ordered Spaces. Springer, Berlin (2003)

    MATH  Google Scholar 

  22. Fu, J.Y.: Generalized vector quasi-equilibrium problems. Math. Mathods Oper. Res. 52, 57–64 (2000)

    Article  MathSciNet  Google Scholar 

  23. Han, Y., Huang, N.J.: Some characterizations of the approximate solutions to generalized vector equilibrium problems. J. Ind. Manag. Optim. 12, 1135–1151 (2016)

    Article  MathSciNet  Google Scholar 

  24. Yen, N.D., Phuong, T.D.: Connectedness and stability of the solution set in linear fractional vector optimization problems. In: Giannessi, F. (ed.) Vector Variational Inequalities and Vector Equilibria, pp. 479–489. Kluwer Academic Publishers, Dordrecht (2000)

    Chapter  Google Scholar 

  25. Michael, E.: Continuous selections: I. Ann. Math. 63(2), 361–382 (1956)

    Article  MathSciNet  Google Scholar 

  26. Tan, N.X., Tinh, P.N.: On the existence of equilibrium points of vector functions. Numer. Funct. Anal. Optim. 19, 141–156 (1998)

    Article  MathSciNet  Google Scholar 

  27. Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton University Press, Princeton (2009)

    Book  Google Scholar 

  28. Wei, H.Z., Chen, C.R., Li, S.J.: Characterizations for optimality conditions of general robust optimization problems. J. Optim. Theory Appl. 177, 835–856 (2018)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant No. 11971078).

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  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    Chong Cui & Shengjie Li

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  1. Chong Cui
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  2. Shengjie Li
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Cui, C., Li, S. Path connectedness of the efficient solution set for generalized vector quasi-equilibrium problems. Optim Lett 16, 1881–1893 (2022). https://doi.org/10.1007/s11590-021-01809-x

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