Geodesic
Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 11, pp. 1788-1803

Voir la notice de l'article provenant de la source Math-Net.Ru

For a pair of dual (possibly improper) linear programming problems, a family of matrix corrections is studied that ensure the existence of given solutions to these problems. The case of correcting the coefficient matrix and three cases of correcting an augmented coefficient matrix (obtained by adding the right-hand side vector of the primal problem, the right-hand-side vector of the dual problem, or both vectors) are considered. Necessary and sufficient conditions for the existence of a solution to the indicated problems, its uniqueness is proved, and the form of matrices for the solution with a minimum Euclidean norm is presented. Numerical examples are given. 
@article{ZVMMF_2017_57_11_a3,
     author = {V. V. Volkov and V. I. Erokhin and A. S. Krasnikov and A. V. Razumov and M. N. Khvostov},
     title = {Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1788--1803},
     publisher = {mathdoc},
     volume = {57},
     number = {11},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_11_a3/}
}
TY  - JOUR
AU  - V. V. Volkov
AU  - V. I. Erokhin
AU  - A. S. Krasnikov
AU  - A. V. Razumov
AU  - M. N. Khvostov
TI  - Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2017
SP  - 1788
EP  - 1803
VL  - 57
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_11_a3/
LA  - ru
ID  - ZVMMF_2017_57_11_a3
ER  - 
%0 Journal Article
%A V. V. Volkov
%A V. I. Erokhin
%A A. S. Krasnikov
%A A. V. Razumov
%A M. N. Khvostov
%T Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2017
%P 1788-1803
%V 57
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_11_a3/
%G ru
%F ZVMMF_2017_57_11_a3
V. V. Volkov; V. I. Erokhin; A. S. Krasnikov; A. V. Razumov; M. N. Khvostov. Minimum-Euclidean-norm matrix correction for a pair of dual linear programming problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 11, pp. 1788-1803. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_11_a3/