Iterative regularization method with a proximal operator (Q1974712)

The author considers the mathematical programming problem of finding an element \(y\in H\), a Hilbert space, such that \(f(y)= \inf f(z)\), \(z\in Q\), where \(Q\) is a convex closed set of \(H\). In practice the information about \(f\) and \(Q\) is of approximate character, i.e. instead of \(f\) and \(Q\) we have some function and a set \(Q_n\). A version of the Bakushinskij-Polyak method with a proximal operator is used for solving an unstable approximate mathematical programming problem with constraints in the Hilbert space \(H\). A new form of the regularization operator is proposed and based on this result minimizing sequence \(z_n\) has been constructed such that \(\lim_{n\to\infty}\|z_n-y\|= 0\).