Genericity and Hölder Stability in Semi-Algebraic Variational Inequalities

  • Jae Hyoung Lee
  • Gue Myung Lee
  • Tiến-Sơn Phạm


The aim of this paper is twofold. We first present generic properties of semi-algebraic variational inequalities: “typical” semi-algebraic variational inequalities have finitely many solutions, around each of which they admit a unique “active manifold” and such solutions are nondegenerate. Second, based on these results, we offer Hölder stability, upper semi-continuity, and lower semi-continuity properties of the solution map of parameterized variational inequalities.


Genericity Hölder stability Semi-algebraic variational inequality 

Mathematics Subject Classification

90C26 90C31 14P10 49K40 



The authors would like to thank the referees for careful reading and constructive comments. A part of this work was done while the third author was visiting Department of Applied Mathematics, Pukyong National University, Busan, Korea, in September 2016. He would like to thank the department for the hospitality and support during his stay. The second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2017R1E1A1A03069931). The third author is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.04-2016.05


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Copyright information

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

Authors and Affiliations

  • Jae Hyoung Lee
    • 1
  • Gue Myung Lee
    • 1
  • Tiến-Sơn Phạm
    • 2
  1. 1.Department of Applied MathematicsPukyong National UniversityBusanRepublic of Korea
  2. 2.Department of MathematicsUniversity of DalatDalatVietnam

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