On the choice of parameters in the quasisolution method for the correction of improper convex programs

The paper is devoted to finding approximation solutions of improper convex programs. For such programs, a correction model is considered in the form of the problem of minimizing the objective function of the original problem on the set of extremal points of a penalty function, which aggregates the inconsistent constraints. For the penalty function, the Eremin–Zangwill exact penalty function is chosen. Under an approximately given input, a generalized solution of the improper convex program is obtained by applying the quasisolution method known in the theory of ill-posed problems. Estimates characterizing the quality of the correction are given. Iterative schemes implementing this approach are proposed.