Using a priori information about a solution of an ill-posed problem for constructing regularizing algorithms and their applications

In this article ill-posed problems with some a priori information about the exact solution are considered. For the first group of problems, we assume that the solution belongs to some compact set (e.g., monotonic or convex bounded functions). For the second group, we suppose that the exact solution is sourcewise represented. The algorithms to construct an approximate solution and to estimate its error are described.