Interval regularization, recognizing functional, and non-smooth optimization technique

摘要

The subject matter of the paper is application of the convex non-smooth optimization methods. More precisely, we consider a procedure of interval regularization with recognizing functional technique. The procedure reduces the solution of the imprecise linear system of equations to computing a point from the tolerable solution set for the interval system. It is necessary to maximize the recognizing functional of the interval system for computing the point. Efficient maximization of the recognizing functional is a convex optimization problem with non-smooth objective function. Moreover, the concept of a tolerable pseudosolution to an interval system of linear algebraic equations is used. Our results showed that interval regularization problems can be solved in practice not only as a related linear programming problems, but also by non-smooth optimization methods. The last way may be the only one for finding the solutions of large- and huge-scale problems.