On the optimal correction of contradictory problems of convex programming

Some problems arising from the application of the regularized Lagrange function method for the optimal correction of convex programming problems in which the system of constraints can be contradictory are considered. Among the problems under consideration, there are the existence of an optimal correction vector, feasibility of an approximating problem and of the problem dual to it, and issues related to the regularization of improper problems. Agreement conditions for the regularization parameters and approximation error are established and convergence estimates are given.