Some Remarks on Stability of Generalized Equations

The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the solution map to a class of generalized equations, where the multivalued term amounts to the regular normal cone to a (possibly nonconvex) set given by C 2 inequalities. Instead of the linear...

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Veröffentlicht in:Journal of optimization theory and applications Jg. 159; H. 3; S. 681 - 697
Hauptverfasser: Henrion, René, Kruger, Alexander Y., Outrata, Jiří V.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.12.2013
Springer Nature B.V
Schlagworte:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematical analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Studies
Theory of Computation
Regular and limiting coderivative
Mathematical program with equilibrium constraints
Parameterized generalized equation
Constant rank CQ
ISSN:0022-3239, 1573-2878
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Zusammenfassung:The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the solution map to a class of generalized equations, where the multivalued term amounts to the regular normal cone to a (possibly nonconvex) set given by C 2 inequalities. Instead of the linear independence qualification condition, standardly used in this context, one assumes a combination of the Mangasarian–Fromovitz and the constant rank qualification conditions. Based on the obtained generalized derivatives, new optimality conditions for a class of mathematical programs with equilibrium constraints are derived, and a workable characterization of the isolated calmness of the considered solution map is provided.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0147-x