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Generalized B-Well-Posedness for Set Optimization Problems

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Abstract

This paper aims at studying the generalized well-posedness in the sense of Bednarczuk for set optimization problems with set-valued maps. Three kinds of B-well-posedness for set optimization problems are introduced. Some relations among the three kinds of B-well-posedness are established. Necessary and sufficient conditions of well-posedness for set optimization problems are obtained.

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Acknowledgements

The authors would like to thank the editor and anonymous referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (11001287 and 11171363), the Natural Science Foundation Project of Chongqing (CSTC 2010BB9254 and CSTC 2009BB8240), the Education Committee Project Research Foundation of Chongqing (No. KJ100711), and the Special Fund of Chongqing Key Laboratory (CSTC 2011KLORSE01).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, P.R. China

    X. J. Long

  2. Department of Mathematics, Chongqing Normal University, Chongqing, 400047, P.R. China

    J. W. Peng

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  1. X. J. Long
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Correspondence to J. W. Peng.

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Communicated by Johannes Jahn.

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Long, X.J., Peng, J.W. Generalized B-Well-Posedness for Set Optimization Problems. J Optim Theory Appl 157, 612–623 (2013). https://doi.org/10.1007/s10957-012-0205-4

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