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On the solution continuity of parametric set optimization problems

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Abstract

The aim of this paper is to investigate the continuity of the solution set maps of set-valued vector optimization problems with set optimization criterion. First, we introduce a new concept, which is called a u-lower level map. Then, we give some sufficient conditions for the upper and lower semicontinuities of the generalized lower level map. Finally, by virtue of the semicontinuity of the u-lower level map, we obtain the continuity of the minimal solution set map to parametric set-valued vector optimization problems with set optimization criterion.

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Authors and Affiliations

  1. College of Science, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Y. D. Xu

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

    S. J. Li

Authors
  1. Y. D. Xu
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  2. S. J. Li
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Corresponding author

Correspondence to Y. D. Xu.

Additional information

The authors would like to express their deep gratitude to the anonymous referees for their valuable comments and suggestions, which helped to improve the paper. This research was supported by the National Natural Science Foundation of China (Grant Numbers: 11426055, 11571055, 61472056) and Basic and Advanced Research Project of CQ CSTC (Grant Number: cstc2014jcyjA00044). The Science and Technology Research Project of Chongqing Municipal Education Commission (Grant Number: KJ1500419).

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Xu, Y.D., Li, S.J. On the solution continuity of parametric set optimization problems. Math Meth Oper Res 84, 223–237 (2016). https://doi.org/10.1007/s00186-016-0541-5

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  • DOI: https://doi.org/10.1007/s00186-016-0541-5

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