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Hadamard well-posedness for a set-valued optimization problem

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Abstract

In this paper, we introduce a kind of Hadamard well-posedness for a set-valued optimization problem. By virtue of a scalarization function, we obtain some relationships between weak \({(\varepsilon, e)}\) -minimizers of the set-valued optimization problem and \({\varepsilon}\) -approximate solutions of a scalar optimization problem. Then, we establish a scalarization theorem of P.K. convergence for sequences of set-valued mappings. Based on these results, we also derive a sufficient condition of Hadamard well-posedness for the set-valued optimization problem.

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Author notes

  1. J. Zeng

    Present address: College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

Authors and Affiliations

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

    J. Zeng, S. J. Li & X. W. Xue

  2. Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 610074, China

    W. Y. Zhang

Authors
  1. J. Zeng
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  2. S. J. Li
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  3. W. Y. Zhang
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  4. X. W. Xue
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Correspondence to S. J. Li.

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Zeng, J., Li, S.J., Zhang, W.Y. et al. Hadamard well-posedness for a set-valued optimization problem. Optim Lett 7, 559–573 (2013). https://doi.org/10.1007/s11590-011-0439-3

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  • DOI: https://doi.org/10.1007/s11590-011-0439-3

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