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Genericity and Hölder Stability in Semi-Algebraic Variational Inequalities

Author

Listed:
  • Jae Hyoung Lee

    (Pukyong National University)

  • Gue Myung Lee

    (Pukyong National University)

  • Tiến-Sơn Phạm

    (University of Dalat)

Abstract

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.

Suggested Citation

  • Jae Hyoung Lee & Gue Myung Lee & Tiến-Sơn Phạm, 2018. "Genericity and Hölder Stability in Semi-Algebraic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 56-77, July.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:1:d:10.1007_s10957-018-1234-4
    DOI: 10.1007/s10957-018-1234-4
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    References listed on IDEAS

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    1. Alexander Shapiro, 2005. "Sensitivity Analysis of Parameterized Variational Inequalities," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 109-126, February.
    2. Jérôme Bolte & Aris Daniilidis & Adrian S. Lewis, 2011. "Generic Optimality Conditions for Semialgebraic Convex Programs," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 55-70, February.
    3. J. E. Spingarn & R. T. Rockafellar, 1979. "The Generic Nature of Optimality Conditions in Nonlinear Programming," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 425-430, November.
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