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Metric subregularity and calmness for nonconvex generalized equations in Banach spaces. (English) Zbl 1229.90220
The authors discuss metric subregularity of the generalized equation \[ b\in F(x) ,\tag{GE} \] where \(F:X\rightrightarrows Y\) is a closed multifunction, \(b\in Y\) is a given point and \(X,Y\) are Banach spaces.
They employ variational analysis techniques to provide sufficient and/or necessary conditions for a generalized equation to have the metric subregularity in general Banach spaces.
The conditions are described in terms of coderivatives of the concerned multifunction at points outside the solution set.

MSC:
90C31 Sensitivity, stability, parametric optimization
90C25 Convex programming
49J52 Nonsmooth analysis
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