On a regularization method for improper linear programs

Abstract

We continue the study of alternative duality formation schemes in linear programming based on the symmetric regularization of the Lagrange function simultaneously in the primal and dual variables. A feature of this work is the use of non-Euclidean stabilizing norms. Symmetric bounds for the error of the resulting solution are obtained for the new schemes. The properties of the method are investigated in the case where the constraint system of the original problem is inconsistent. For such problems (improper problems of the first kind), the method gives their generalized solution with an appropriate interpretation. For the improper case, we derive similar estimates for the deviation of the regularized solution from the generalized solution. © 2019 Krasovskii Institute of Mathematics and Mechanics. All rights reserved.