On the application of a regularization method for the correction of improper problems of convex programming

The residual method, which is one of the standard regularization procedures for ill-posed optimization problems, is applied to a convex programming problem. The connection between this method and the regularized Lagrange function method is investigated in the case of optimal correction of improper problems of convex programming. This approach allows one to decrease the number of impropriety classes to be analyzed. Conditions are formulated and convergence estimates of the method are established.