Regularization methods with set extension for solving unstable problems of minimization

Abstract

Some modifications of regularization methods for solving problems of minimization with inaccurate input data are proposed on the basis of the approach of set extension. The consistency conditions for characteristics of errors in restrictions (that define the set) with the stabilizer of the problem are weakened. This allows us to construct regularized problems from the same class the original problem belongs to. For example, if the original problem is a problem of linear programming, then the regularized problem are those from the same class. The convergence of the fundamental regularization methods of stabilization, residues, and quasisolutions is studied; a regularizing operator is constructed.