Calculus rules of the generalized contingent derivative and applications to set-valued optimization

Abstract

In the paper, we develop sum and chain rules of the generalized contingent derivative for set-valued mappings. Then, their applications to sensitivity analysis and optimality conditions for some particular optimization problems are given. Our results extend some recent existing ones in the literature.

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Acknowledgements

This research was funded by Vietnam National University Hochiminh City (VNU-HCM) under Grant Number B2018-28-02. We are thankful to the anonymous referee for his useful comments to improve the manuscript.

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Correspondence to Nguyen Le Hoang Anh.

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Anh, N.L.H., Thoa, N.T. Calculus rules of the generalized contingent derivative and applications to set-valued optimization. Positivity 24, 81–94 (2020). https://doi.org/10.1007/s11117-019-00667-3

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Keywords

  • Generalized contingent derivative
  • Sum rule
  • Chain rule
  • Set-valued optimization
  • Optimality conditions
  • Sensitivity analysis

Mathematics Subject Classification

  • 49J53
  • 90C29
  • 90C46