On Stability of M-stationary Points in MPCCs

We consider parameterized Mathematical Programs with Complementarity Constraints arising, e.g., in modeling of deregulated electricity markets. Using the standard rules of the generalized differential calculus we analyze qualitative stability of solutions to the respective M-stationarity conditions....

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Bibliographic Details
Published in:Set-valued and variational analysis Vol. 22; no. 3; pp. 575 - 595
Main Authors: Červinka, Michal, Outrata, Jiří V., Pištěk, Miroslav
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.09.2014
Subjects:
Analysis
Mathematics
Mathematics and Statistics
Optimization
90C31
Sensitivity analysis
49K40
90C33
Aubin property
Parameterized mathematical programs with complementarity constraints
Isolated calmness
M-stationarity
ISSN:1877-0533, 1877-0541
Online Access:Get full text
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Summary:We consider parameterized Mathematical Programs with Complementarity Constraints arising, e.g., in modeling of deregulated electricity markets. Using the standard rules of the generalized differential calculus we analyze qualitative stability of solutions to the respective M-stationarity conditions. In particular, we provide characterizations and criteria for the isolated calmness and the Aubin properties of the stationarity map. To this end, we introduce the second-order limiting coderivative of mappings and provide formulas for this notion and for the graphical derivative of the limiting coderivative in the case of the normal cone mapping to ℝ + m .
ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-014-0278-3