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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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