Geodesic
On the adaptation of the least squares method to improper problems of mathematical programming
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 247-255

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

We propose a modification of the least squares method, which allows to apply this method not only to usual feasible problems but also to improper problems of mathematical programming of the first kind. The method constructs the usual solution for feasible problems and a generalized solution for improper problems; the generalized solution has a very useful meaningful interpretation. We describe the algorithm, characterize the generalized solution, prove convergence theorems, and present results of numerical experiments.
Keywords: mathematical programming, improper problems, generalized solutions, least squares method. 
@article{TIMM_2013_19_2_a23,
     author = {L. D. Popov},
     title = {On the adaptation of the least squares method to improper problems of mathematical programming},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {247--255},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a23/}
}
TY  - JOUR
AU  - L. D. Popov
TI  - On the adaptation of the least squares method to improper problems of mathematical programming
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2013
SP  - 247
EP  - 255
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a23/
LA  - ru
ID  - TIMM_2013_19_2_a23
ER  - 
%0 Journal Article
%A L. D. Popov
%T On the adaptation of the least squares method to improper problems of mathematical programming
%J Trudy Instituta matematiki i mehaniki
%D 2013
%P 247-255
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a23/
%G ru
%F TIMM_2013_19_2_a23
L. D. Popov. On the adaptation of the least squares method to improper problems of mathematical programming. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 247-255. http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a23/