Regularization methods for solving unstable minimization problems of the first kind with an inaccurately given set. (Q1852521)

The author considers the minimization of a function \(J(u)\) on a set \(U\), which can be briefly written as \(J(u) \rightarrow\inf\), \(u\in U\). Two regularization methods are suggested for this minimization problem in which not only the objective function but also the set where the infimum is sought are given inaccurately. The convergence of the methods is analyzed.