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.


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