Zheng, Xi Yin; Ng, Kung Fu Metric subregularity and calmness for nonconvex generalized equations in Banach spaces. (English) Zbl 1229.90220 SIAM J. Optim. 20, No. 5, 2119-2136 (2010). 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. Reviewer: I. M. Stancu-Minasian (Bucureşti) Cited in 49 Documents MSC: 90C31 Sensitivity, stability, parametric optimization 90C25 Convex programming 49J52 Nonsmooth analysis Keywords:metric subregularity; calmness; coderivative; normal cone; normal dual mapping PDF BibTeX XML Cite \textit{X. Y. Zheng} and \textit{K. F. Ng}, SIAM J. Optim. 20, No. 5, 2119--2136 (2010; Zbl 1229.90220) Full Text: DOI Link OpenURL