Stability Property in Bifunction-Set Optimization

Article

Abstract

This paper gives sufficient conditions for the lower and upper semicontinuities of the solution mapping of a model, called the parametric bifunction-set optimization problem, which provides a bridge between several parametric set optimization problems and parametric generalized vector Ky Fan inequality problems. Our main theorems, applied to the just mentioned problems, give some new or sharper results.

Keywords

Bifunction-set optimization Set optimization Ky Fan inequality Set-valued map Semicontinuity 

Mathematics Subject Classification

90C29 49J40 49K40 

Notes

Acknowledgements

The author would like to thank the anonymous referees for their suggestions, that improved the paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2017.08.

Compliance with Ethical Standards

Conflict of Interest

The author declares that he has no conflict of interest.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam

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