Metric subregularity and calmness for nonconvex generalized equations in Banach spaces. (English) Zbl 1229.90220

Zheng, Xi Yin; Ng, Kung Fu

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)

MSC:

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

Keywords:

metric subregularity; calmness; coderivative; normal cone; normal dual mapping