Application of nonsmooth optimization methods to solving nonlinear operator equations (Q1571234)

The authors analyse the noise stability of subgradient-type methods as applied to determining regular and singular solutions to nonlinear operator equation in Hilbert spaces \(X,Y:F(x)=0\) with the operator \(F:X\rightarrow{Y}\) that is Fréchet differentiable. It is shown that all conditions for implementing the developed iterative process are fulfilled and the noise errors are sufficiently small.