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Painlevé-Kuratowski Stability of the Solution Sets to Perturbed Vector Generalized Systems

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Abstract

In this paper, stability results of solution mappings to perturbed vector generalized system are studied. Firstly, without the assumption of monotonicity, the Painlevé-Kuratowski convergence of global efficient solution sets of a family of perturbed problems to the corresponding global efficient solution set of the generalized system is obtained, where the perturbations are performed on both the objective function and the feasible set. Then, the density and Painlevé-Kuratowski convergence results of efficient solution sets are established by using gamma convergence, which is weaker than the assumption of continuous convergence. These results extend and improve the recent ones in the literature.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing JiaoTong University, Chongqing, 400074, China

    Zai-yun Peng & Yong Zhao

  2. Department of Mathematics, Sichuan University, Chengdu, 610064, China

    Yong Zhao

  3. Department of Mathematics, Chongqing Normal University, Chongqing, 400047, China

    Xin-min Yang

Authors
  1. Zai-yun Peng
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  2. Yong Zhao
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  3. Xin-min Yang
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Correspondence to Zai-yun Peng.

Additional information

Supported by the National Natural Science Foundation of China (No.11431004.11471059.11401058), the Basic and Advanced Research Project of Chongqing (cstc2017jcyjAX0382,cstc2015shmszx30004), the Program for University Innovation Team of Chongqing (CXTDX201601022) and the Education Committee Project Foundation of Bayu Scholar).

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Peng, Zy., Zhao, Y. & Yang, Xm. Painlevé-Kuratowski Stability of the Solution Sets to Perturbed Vector Generalized Systems. Acta Math. Appl. Sin. Engl. Ser. 34, 304–317 (2018). https://doi.org/10.1007/s10255-018-0743-0

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  • DOI: https://doi.org/10.1007/s10255-018-0743-0

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