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.
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By semialgebraic function, we mean any function whose graph can be described by finitely many intersections and unions of polynomial sublevel sets or level sets.
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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.
Tiến Sơn Phạm was partially supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED), Grant 101.04-2016.05. Xuân Ɖức Hà Trương was partially supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED). Jen-Chih Yao was partially supported by the Grant MOST 105-2115-M-039-002-MY3.
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Phạm, T.S., Trương, X.Ɖ.H. & Yao, J. The global weak sharp minima with explicit exponents in polynomial vector optimization problems. Positivity 22, 219–244 (2018). https://doi.org/10.1007/s11117-017-0509-6
- Global weak sharp minima with explicit exponents
- Vector optimization
Mathematics Subject Classification