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Positivity

, Volume 22, Issue 1, pp 219–244 | Cite as

The global weak sharp minima with explicit exponents in polynomial vector optimization problems

  • Tiến Sơn Phạm
  • Xuân Ɖức Hà Trương
  • Jen-Chih Yao
Article

Abstract

In this paper we discuss the global weak sharp minima property for vector optimization problems with polynomial data. Exploiting the imposed polynomial structure together with tools of variational analysis and a quantitative version of Łojasiewicz’s gradient inequality due to D’Acunto and Kurdyka, we establish the Hölder type global weak sharp minima with explicitly calculated exponents.

Keywords

Global weak sharp minima with explicit exponents Vector optimization Polynomials 

Mathematics Subject Classification

49J53 58C06 90C29 

Notes

Acknowledgements

The authors would like to thank the editor and the referees for useful remarks and comments which allow to improve the paper. This work was performed during research visits of the first and the second authors at the Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan and at the Vietnam Institute for Advanced Study of Mathematics. These authors wish to thank the mentioned organizations for hospitality and support.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Tiến Sơn Phạm
    • 1
    • 2
  • Xuân Ɖức Hà Trương
    • 3
  • Jen-Chih Yao
    • 4
  1. 1.Division of Computational Mathematics and Engineering, Institute for Computational ScienceTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam
  4. 4.Center for General Education, China Medical UniversityTaichungTaiwan

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