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Stability of Set-Valued Optimization Problems with Naturally Quasi-Functions

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Abstract

In this paper, we discuss the stability of three kinds of minimal point sets and three kinds of minimizer sets of naturally quasi-functional set-valued optimization problems when the data of the approximate problems converges to the data of the original problems in the sense of Painlevé–Kuratowski. Our main results improve and extend the results of the recent papers.

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Acknowledgments

This research was partially supported by the National Natural Science Foundation of China (11201509 and 11271389), the Basic and Advanced Research Project of Chongqing (cstc2014jcyjA00046), the Education Committee Project Research Foundation of Chongqing (KJ1400304) and the Program for Core Young Teacher of the Municipal Higher Education of Chongqing ([2014]47). The authors would like to express their deep gratitude to the anonymous referees and the associate editor for their valuable comments and suggestions which helped to improve the paper.

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Authors and Affiliations

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

    Xiao-Bing Li, Qi-Lin Wang & Zhi Lin

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  1. Xiao-Bing Li
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  2. Qi-Lin Wang
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  3. Zhi Lin
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Correspondence to Xiao-Bing Li.

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Communicated by Jafar Zafarani.

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Li, XB., Wang, QL. & Lin, Z. Stability of Set-Valued Optimization Problems with Naturally Quasi-Functions. J Optim Theory Appl 168, 850–863 (2016). https://doi.org/10.1007/s10957-015-0802-0

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  • DOI: https://doi.org/10.1007/s10957-015-0802-0

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