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Lagrangian conditions for approximate solutions on nonconvex set-valued optimization problems

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Abstract

The purpose of this paper is to consider the set-valued optimization problem in Asplund spaces without convexity assumption. By a scalarization function introduced by Tammer and Weidner (J Optim Theory Appl 67:297–320, 1990), we obtain the Lagrangian condition for approximate solutions on set-valued optimization problems in terms of the Mordukhovich coderivative.

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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

    X. J. Long & J. Zeng

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

    X. B. Li

Authors
  1. X. J. Long
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  2. X. B. Li
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  3. J. Zeng
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Correspondence to X. J. Long.

Additional information

This work was supported by the National Natural Science Foundation of China (11001287), the Natural Science Foundation Project of Chongqing (CSTC 2010BB9254) and the Education Committee Project Research Foundation of Chongqing (No. KJ100711).

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Long, X.J., Li, X.B. & Zeng, J. Lagrangian conditions for approximate solutions on nonconvex set-valued optimization problems. Optim Lett 7, 1847–1856 (2013). https://doi.org/10.1007/s11590-012-0527-z

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