Geodesic
On active-set methods for the quadratic programming problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 4, pp. 602-613 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The active-set Newton method developed earlier by the authors for mixed complementarity problems is applied to solving the quadratic programming problem with a positive definite matrix of the objective function. A theoretical justification is given to the fact that the method is guaranteed to find the exact solution in a finite number of steps. Numerical results indicate that this approach is competitive with other available methods for quadratic programming problems. 
@article{ZVMMF_2012_52_4_a2,
     author = {A. N. Daryina and A. F. Izmailov},
     title = {On active-set methods for the quadratic programming problem},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {602--613},
     year = {2012},
     volume = {52},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_4_a2/}
}
TY  - JOUR
AU  - A. N. Daryina
AU  - A. F. Izmailov
TI  - On active-set methods for the quadratic programming problem
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2012
SP  - 602
EP  - 613
VL  - 52
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_4_a2/
LA  - ru
ID  - ZVMMF_2012_52_4_a2
ER  - 
%0 Journal Article
%A A. N. Daryina
%A A. F. Izmailov
%T On active-set methods for the quadratic programming problem
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2012
%P 602-613
%V 52
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_4_a2/
%G ru
%F ZVMMF_2012_52_4_a2
A. N. Daryina; A. F. Izmailov. On active-set methods for the quadratic programming problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 4, pp. 602-613. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_4_a2/

[1] Izmailov A. F., Solodov M. F., Chislennye metody optimizatsii, Izd. 2-e, pererab. i dop., Fizmatlit, M., 2008

[2] Klark F., Optimizatsiya i negladkii analiz, Nauka, M., 1988 | MR | Zbl

[3] Sukharev A. G., Timokhov A. V., Fedorov V. V., Kurs metodov optimizatsii, Nauka, M., 1986 | MR | Zbl

[4] Daryina A. N., Izmailov A. F., Solodov M. V., “Numerical results for a globalized active-set Newton method for mixed complementarity problems”, Comput. Appl. Math., 24:2 (2005), 293–316 | DOI | MR | Zbl

[5] Daryina A. N., Izmailov A. F., Solodov M. V., “A class of active-set Newton methods for mixed complementarity problem”, SIAM J. Optim., 15:2 (2004), 409–429 | DOI | MR | Zbl

[6] Darina A. N., Izmailov A. F., Solodov M. V., “Smeshannye komplementarnye zadachi: regulyarnost, otsenki rasstoyaniya do resheniya i nyutonovskie metody”, Zh. vychisl. matem. matem. fiz., 44:1 (2004), 51–69 | MR

[7] Voevodin V. V., Vychislitelnye osnovy lineinoi algebry, Nauka, M., 1977 | MR | Zbl

[8] Billups S. C., Algorithms for complementarity problems and generalized equations, PhD thesis, Madison, 1995, 159 pp. | MR

[9] Tseng P., “Growth behavior of a class of merit functions for the nonlinear complementarity problem”, J. Optimizat. Theory Appl., 89 (1996), 17–37 | DOI | MR | Zbl

[10] Kanzow C., Fukushima M., “Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities”, Math. Program., 83 (1998), 55–87 | MR | Zbl

[11] Peng J.-M., “Equivalence of variational inequality problems to unconsrtained optimization”, Math. Program., 78 (1997), 347–355 | MR | Zbl

[12] Billups S. C., “A homothopy-based algorithm for mixed complementarity problems”, SIAM J. Optimizat., 12:3 (2002), 583–605 | DOI | MR | Zbl

[13] De Luca T., Facchinei F., Kanzow C., “A theoretical and numerical comparison of some semismooth algorithms for complementarity problems”, Comput. Optim. Appl., 16 (2000), 173–205 | DOI | MR | Zbl

[14] Darina A. N., Izmailov A. F., “Polugladkii metod Nyutona dlya zadachi kvadratichnogo programmirovaniya s prostymi ogranicheniyami”, Zh. vychisl. matem. matem. fiz., 49:10 (2009), 1785–1795 | MR

[15] Dolan E., Moré J., “Benchmarking optimization software with performance profiles”, Math. Program., 91:2 (2002), 201–213 | DOI | MR | Zbl

[16] Nocedal J., Wright S. J., Numerical optimization, Second edition, Springer, New York, 2006 | MR