Genericity and Hölder Stability in Semi-Algebraic Variational Inequalities

Genericity and Hölder Stability in Semi-Algebraic Variational Inequalities

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, b...

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Veröffentlicht in:Journal of optimization theory and applications 2018-07, Vol.178 (1), p.56-77
Hauptverfasser: Lee, Jae Hyoung, Lee, Gue Myung, Phạm, Tiến-Sơn
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Continuity
Cybernetics
Engineering
Estimates
Inequalities
Mathematical analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Stability
Theory of Computation
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Beschreibung
Zusammenfassung: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1234-4