Genericity and Hölder Stability in Semi-Algebraic Variational Inequalities

Jae Hyoung Lee (), Gue Myung Lee () and Tiến-Sơn Phạm ()
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Jae Hyoung Lee: Pukyong National University
Gue Myung Lee: Pukyong National University
Tiến-Sơn Phạm: University of Dalat

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 1, No 4, 56-77

Abstract: 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.

Keywords: Genericity; Hölder stability; Semi-algebraic variational inequality; 90C26; 90C31; 14P10; 49K40 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1234-4

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