The perturbed proximal point algorithm and some of its applications (Q1317307)

The scope of the paper is to study the proximal point algorithm, i.e. solving the inclusion \(0 \in T \overline x\) by computing a sequence \(\{x^ n\}\) with \(x^{n+1} =(I+\lambda T)^{-1} x^ n\). Here \(T\) is a maximal monotone operator on a Hilbert space \(H\). The main results give conditions under which, if \(x^{n+1} = (I+\lambda T^ n)^{-1} x^ n+e^ n\), where \(T^ n\) is a perturbation of \(T\) and \(e^ n\) is an error term, the sequence still converges to a solution. The size of the perturbation is given in terms of a certain variational matrix. Numerical results are provided.