On a regularization method for improper linear programs
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 1, pp. 196-206
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
Keywords:
linear programming, duality, regularization methods, accuracy of the solution.
@article{TIMM_2019_25_1_a14,
author = {L. D. Popov},
title = {On a regularization method for improper linear programs},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {196--206},
publisher = {mathdoc},
volume = {25},
number = {1},
year = {2019},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2019_25_1_a14/}
}
L. D. Popov. On a regularization method for improper linear programs. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 1, pp. 196-206. http://geodesic.mathdoc.fr/item/TIMM_2019_25_1_a14/