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On the stability of solutions for semi-infinite vector optimization problems

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Abstract

This paper is concerned with the stability of semi-infinite vector optimization problems (SVO). Under weak assumptions, we establish sufficient conditions of the Berge-lower semicontinuity and lower Painlev\(\acute{e}\)–Kuratowski convergence of weak efficient solutions for (SVO) under functional perturbations of both objective functions and constraint sets. Some examples are given to illustrate that our results are new and interesting.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (11301571,11471059), the Basic and Advanced Research Project of Chongqing (cstc2015jcyjB00001, cstc 464 2015jcyjBX0029), cstc2017jcyjAX0382 the China Postdoctoral Science Foundation funded project (2016T90837,2015M580774), the Program for University Innovation Team of Chongqing (CXTDX201601022,CXTDX201601026) and the Education Committee Project Foundation of Bayu Scholar. The authors are grateful to the editor and two anonymous referees for valuable comments and suggestions to improve the paper.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing JiaoTong University, Chongqing, 400074, People’s Republic of China

    Zai-Yun Peng

  2. Department of Mathematics, Chongqing Normal University, Chongqing, 400047, People’s Republic of China

    Jian-Wen Peng

  3. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, People’s Republic of China

    Xian-Jun Long

  4. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Jen-Chih Yao

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  1. Zai-Yun Peng
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  2. Jian-Wen Peng
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  3. Xian-Jun Long
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  4. Jen-Chih Yao
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Correspondence to Jian-Wen Peng.

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Peng, ZY., Peng, JW., Long, XJ. et al. On the stability of solutions for semi-infinite vector optimization problems. J Glob Optim 70, 55–69 (2018). https://doi.org/10.1007/s10898-017-0553-6

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  • DOI: https://doi.org/10.1007/s10898-017-0553-6

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