A random direction algorithm for an intersection problem (Q1195959)

Let \(C_ 1,C_ 2,\dots,C_ p\) be \(p\) closed convex subsets of a Hilbert space \(H\) such that \(\cap^ p C_ i \neq \emptyset\). Let \(P_ i\) denote the projection map of \(H\) onto \(C_ i\). The authors discuss the convergence of the sequence \(x_ n\) generated as follows: starting from any \(x_ 0\in H\), let \(x_ n\) (\(n \in N\)) be defined by \(x_{n+1} = p_ ix_ n\), where \(i \in \{1,2,\dots,p\}\) is chosen randomly. A nonlinear successive overrelaxation type algorithm is established.