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Connectedness of Approximate Efficient Solutions for Generalized Semi-Infinite Vector Optimization Problems

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Abstract

In this paper, the approximate efficient solution of generalized semi-infinite vector optimization problems is considered. Utilizing the density of approximate efficient points, the convexity and upper semicontinuity of constraint set mapping, we establish the connectedness of the set of approximate efficient points and the set of approximate efficient solutions to generalized semi-infinite vector optimization problems with set-valued objective maps in normed spaces. As applications, the connectedness of the solution set for semi-infinite vector optimization problems and generalized nonlinear programming problems are also obtained, respectively. Our results are new and extend the results by Gong and the results by Li.

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Acknowledgments

The first author was partially supported by the National Natural Science Foundation of China (11301571.11471059), and the Basic and Advanced Research Project of Chongqing (cstc2015jcyjBX0131), the China Postdoctoral Science Foundation funded project (2016T90837), the Program for University Innovation Team of Chongqing (CXTDX201601022) and the Education Committee Project Foundation of Bayu Scholar. The second author author was supported by the Natural Sciences and Engineering Research Council of Canada. The last author was supported by the National Natural Science Foundation of China (11431004) and the Natural Science Foundation of Chongqing (cstc2014pt-sy00001). The authors are grateful to 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, University of British Columbia, Kelowna, BC, V1V 1V7, Canada

    Xianfu Wang

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

    Xin-Min Yang

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  1. Zai-Yun Peng
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  2. Xianfu Wang
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  3. Xin-Min Yang
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Correspondence to Zai-Yun Peng.

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Peng, ZY., Wang, X. & Yang, XM. Connectedness of Approximate Efficient Solutions for Generalized Semi-Infinite Vector Optimization Problems. Set-Valued Var. Anal 27, 103–118 (2019). https://doi.org/10.1007/s11228-017-0423-x

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  • DOI: https://doi.org/10.1007/s11228-017-0423-x

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