Constrained Convex Minimization Methods Generating Regularizing Algorithms

We propose a modified version of a previously published iterative method for solving a minimization problem of a convex function. This modification involves a new procedure for computing the metric projection which is included in the step operator of the basis iterative process. Unlike the original method, the modified version allows for solving the constrained convex minimization problem for both consistent and inconsistent systems of constraints. The convergence of the iterative process and its stability with respect to input data errors are investigated. The performed model numerical examples confirm the effectiveness of the basis and the modified methods.