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Scalarization and pointwise well-posedness for set optimization problems

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Abstract

In this paper, we consider three kinds of pointwise well-posedness for set optimization problems. We establish some relations among the three kinds of pointwise well-posedness. By virtue of a generalized nonlinear scalarization function, we obtain the equivalence relations between the three kinds of pointwise well-posedness for set optimization problems and the well-posedness of three kinds of scalar optimization problems, respectively.

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Acknowledgments

The authors would like to thank the editor and the referees for their valuable comments and suggestions, which have improved the presentation of the paper.

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Authors and Affiliations

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

    Xian-Jun Long

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

    Jian-Wen Peng

  3. College of Science, Chongqing JiaoTong University, Chongqing, 400074, People’s Republic of China

    Zai-Yun Peng

Authors
  1. Xian-Jun Long
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  2. Jian-Wen Peng
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  3. Zai-Yun Peng
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Corresponding author

Correspondence to Jian-Wen Peng.

Additional information

This research was partially supported by the National Natural Science Foundation of China (11471059, 11171363, 11301571 and 11431004), the Basic and Advanced Research Project of Chongqing (cstc2014jcyjA00037), the Education Committee Project Research Foundation of Chongqing (KJ1400618), the Program for Core Young Teacher of the Municipal Higher Education of Chongqing [(2014)47] , the Program for Chongqing Innovation Team in University (KJTD201313) and the Education Committee Project Foundation of Bayu Scholar.

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Long, XJ., Peng, JW. & Peng, ZY. Scalarization and pointwise well-posedness for set optimization problems. J Glob Optim 62, 763–773 (2015). https://doi.org/10.1007/s10898-014-0265-0

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