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Positivity

pp 1–14 | Cite as

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

  • Nguyen Le Hoang AnhEmail author
  • Nguyen Thanh Thoa
Article
  • 19 Downloads

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.

Keywords

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

Mathematics Subject Classification

49J53 90C29 90C46 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Optimization and System TheoryVNUHCM-University of ScienceHochiminh CityVietnam
  2. 2.Faculty of Basic SciencesUniversity of Transport and Communications - Campus in Ho Chi Minh CityHochiminh CityVietnam

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