Geodesic
Finding the projection of a given point on the set of solutions of a linear programming problem
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 2, pp. 33-47 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The problem of finding the projections of points on the sets of solutions of primal and dual problems of linear programming is considered. This problem is reduced to a single solution of the problem of minimizing a new auxiliary function, starting from some threshold value of the penalty coefficient. Estimates of the threshold value are obtained. A software implementation of the proposed method is compared with some known commercial and research software packages for solving linear programming problems. 
@article{TIMM_2008_14_2_a4,
     author = {A. I. Golikov and Yu. G. Evtushenko},
     title = {Finding the projection of a~given point on the set of solutions of a~linear programming problem},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {33--47},
     year = {2008},
     volume = {14},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2008_14_2_a4/}
}
TY  - JOUR
AU  - A. I. Golikov
AU  - Yu. G. Evtushenko
TI  - Finding the projection of a given point on the set of solutions of a linear programming problem
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2008
SP  - 33
EP  - 47
VL  - 14
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMM_2008_14_2_a4/
LA  - ru
ID  - TIMM_2008_14_2_a4
ER  - 
%0 Journal Article
%A A. I. Golikov
%A Yu. G. Evtushenko
%T Finding the projection of a given point on the set of solutions of a linear programming problem
%J Trudy Instituta matematiki i mehaniki
%D 2008
%P 33-47
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/TIMM_2008_14_2_a4/
%G ru
%F TIMM_2008_14_2_a4
A. I. Golikov; Yu. G. Evtushenko. Finding the projection of a given point on the set of solutions of a linear programming problem. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 2, pp. 33-47. http://geodesic.mathdoc.fr/item/TIMM_2008_14_2_a4/

[1] Eremin I. I., Teoriya lineinoi optimizatsii, Izd-vo “Ekaterinburg”, Ekaterinburg, 1999

[2] Vasilev F. P., Ivanitskii A. Yu., Lineinoe programmirovanie, Faktorial Press, M., 2003 | MR

[3] Golikov A. I., Evtushenko Yu. G., “Otyskanie normalnykh reshenii v zadachakh lineinogo programmirovaniya”, Zhurn. vychisl. matematiki i mat. fiziki, 40:12 (2000), 1766–1786 | MR | Zbl

[4] Kanzow C., Qi H., Qi L., “On the minimum norm solution of linear programs”, J. of Optimizat. Theory and Appl., 116 (2003), 333–345 | DOI | MR | Zbl

[5] Golikov A. I., Evtushenko Yu. G., Mollaverdi N., “Primenenie metoda Nyutona k resheniyu zadach lineinogo programmirovaniya bolshoi razmernosti”, Zhurn. vychisl. matematiki i mat. fiziki, 44:9 (2004), 1564–1573 | MR | Zbl

[6] Mangasarian O. L., “A finite Newton method for classification”, Optimizat. Meth. and Software, 17 (2002), 913–930 | DOI | MR

[7] Mangasarian O. L., “A Newton method for linear programming”, J. of Optimizat. Theory and Appl., 121 (2004), 1–18 | DOI | MR | Zbl

[8] Meszaros Cs., “The BPMPD interior point solver for convex quadratic programming problems”, Optimizat. Meth. and Software, 11–12 (1999), 431–449 | DOI | MR | Zbl

[9] Andersen E. D., Andersen K. D., “The MOSEK interior point optimizer for linear programming: an implementation of homogeneous algorithm”, High performance optimization, Kluwer, New York, 2000, 197–232 | MR | Zbl

[10] Popov L. D., “Kvadratichnaya approksimatsiya shtrafnykh funktsii pri reshenii zadach lineinogo programmirovaniya bolshoi razmernosti”, Zhurn. vychisl. matematiki i mat. fiziki, 47:2 (2007), 206–221 | MR | Zbl