Geodesic
Barriers and symmetric regularization of the Lagrange function in the analysis of improper linear programming problems
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 3, pp. 138-155

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

In this paper, the author continues his research on the modification and adaptation of classical methods of the central path in order to apply them to the analysis of improper problems of linear programming. In the new constructions presented in the paper, in contrast to those developed earlier, it becomes possible to apply second-order optimization methods. Moreover, there is no need to specify in advance the type of impropriety of the problem being solved. Convergence theorems for the constructed methods are given, a meaningful interpretation of the obtained generalized solution is provided, and the results of numerical experiments are presented.
Keywords: linear programming, improper problems, generalized solutions, barrier function method, regularization. 
@article{TIMM_2023_29_3_a8,
     author = {L. D. Popov},
     title = {Barriers and symmetric regularization of the {Lagrange} function in the analysis of improper linear programming problems},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {138--155},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2023_29_3_a8/}
}
TY  - JOUR
AU  - L. D. Popov
TI  - Barriers and symmetric regularization of the Lagrange function in the analysis of improper linear programming problems
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2023
SP  - 138
EP  - 155
VL  - 29
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2023_29_3_a8/
LA  - ru
ID  - TIMM_2023_29_3_a8
ER  - 
%0 Journal Article
%A L. D. Popov
%T Barriers and symmetric regularization of the Lagrange function in the analysis of improper linear programming problems
%J Trudy Instituta matematiki i mehaniki
%D 2023
%P 138-155
%V 29
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2023_29_3_a8/
%G ru
%F TIMM_2023_29_3_a8
L. D. Popov. Barriers and symmetric regularization of the Lagrange function in the analysis of improper linear programming problems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 3, pp. 138-155. http://geodesic.mathdoc.fr/item/TIMM_2023_29_3_a8/