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
Online-Zugang:Volltext
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Abstract 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.
AbstractList 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 ^sup 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.[PUBLICATION ABSTRACT]
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.
Author Henrion, René
Kruger, Alexander Y.
Outrata, Jiří V.
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  fullname: Kruger, Alexander Y.
  email: a.kruger@ballarat.edu.au
  organization: Centre for Informatics and Applied Optimization, School of Science, Information Technology and Engineering, University of Ballarat
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  givenname: Jiří V.
  surname: Outrata
  fullname: Outrata, Jiří V.
  organization: Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic
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Cites_doi 10.1007/978-0-387-87821-8
10.1007/978-3-642-02431-3
10.1137/S1052623400371016
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Keywords Regular and limiting coderivative
Mathematical program with equilibrium constraints
Parameterized generalized equation
Constant rank CQ
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A.L. Dontchev (147_CR4) 2001; 12
R. Henrion (147_CR1) 2012
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SubjectTerms 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
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