Iterative behaviour, fixed point of a class of monotone operators. Application to non-symmetric threshold function (Q1104051)

The authors consider the iteration \(x^{KH}=YA^ tXAX^ k\) with \(x^ 0\in {\mathbb{R}}^ n\) arbitrary, where X and Y are subgradients of \(f\in \Gamma_ 0({\mathbb{R}}\) m) and \(g\in \Gamma_ 0({\mathbb{R}}^ n\)), respectively, A is an \(m\times n\) matrix. If f and g are continuous and \(\delta g(0)\supset Y({\mathbb{R}}^ n\)) then \(f(AYA^ tXAx)\geq f(Ax)\) for every A and \(x\in Y({\mathbb{R}}^ n\)). Using this result the convergence of \(\{x^ k\}\) is proved if one of f or g is polyhedral and the corresponding subgradient is discrete.