Geodesic
Fejer algorithms with an adaptive step
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 5, pp. 791-801 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For Fejer processes with attractants, a general adaptive scheme for step multiplier control is proposed and the convergence of this class of algorithms to stationary points is proved. Numerical results demonstrating that the convergence rate is generally linear are presented. 
@article{ZVMMF_2011_51_5_a4,
     author = {E. A. Nurminski},
     title = {Fejer algorithms with an adaptive step},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {791--801},
     year = {2011},
     volume = {51},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_5_a4/}
}
TY  - JOUR
AU  - E. A. Nurminski
TI  - Fejer algorithms with an adaptive step
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 791
EP  - 801
VL  - 51
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_5_a4/
LA  - ru
ID  - ZVMMF_2011_51_5_a4
ER  - 
%0 Journal Article
%A E. A. Nurminski
%T Fejer algorithms with an adaptive step
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 791-801
%V 51
%N 5
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_5_a4/
%G ru
%F ZVMMF_2011_51_5_a4
E. A. Nurminski. Fejer algorithms with an adaptive step. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 5, pp. 791-801. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_5_a4/

[1] Nurminskii E. A., “Ispolzovanie dopolnitelnykh malykh vozdeistvii v feierovskikh modelyakh iterativnykh algoritmov”, Zh. vychisl. matem. i matem. fiz., 48:12 (2008), 2121–2128

[2] Nurminskii E. A., “Feierovskie protsessy c malymi vozmuscheniyami”, Dokl. RAN, 422:5 (2008), 601–604

[3] Nurminski E. A., “Envelope stepsize control for iterative algorithms based on Fejer processes with attractants”, Optmizat. Methods and Software, 25:1 (2010), 97–108

[4] Vasin V. V., Eremin I. I., Operatory i iteratsionnye protsessy feierovskogo tipa. Teoriya i prilozheniya, UrO RAN, Ekaterinburg, 2005

[5] Bauschke H. H., Borwein J. M., “On projection algorithms for solving convex feasibility problems”, SIAM Revs, 38:3 (1996), 367–426

[6] Pshenichnyi B. N., Vypuklyi analiz i ekstremalnye zadachi, Nauka, M., 1980

[7] Nurminskii E. A., Chislennye metody vypukloi optimizatsii, Nauka, M., 1991

[8] Fukushima M., “A relaxed projection method for variational inequalities”, Math. Program., 35 (1986), 58–70

[9] Byrne C. L., “A unified treatment of some iterative algorithms in signal processing and image reconstruction”, Inverse Problems, 20:1 (2004), 103–120

[10] Yang Q., “The relaxed CQ algorithm solving the split feasibility problem”, Inverse Problems, 20:4 (2004), 1261–1266

[11] “Nonsmooth optimization”, Proc. IASA Workshop, March 28–April 8, 1977, Internat. Inst. Appl. Systems Analys. IIASA proc. series, 3, eds. Lemarechal C., Mifflin R., Pergamon Press, Oxford, 1978

[12] Sovmestnyi rossiisko-ukrainskii proekt RFFI (Rossiiskii fond fundamentalnykh issledovanii, Rossiya) i DFFD (Derzhavnii fond fundamentalnikh doslidzhen, Ukraina) “Subgradientnye metody uskorennoi skhodimosti v zadachakh vypuklogo programmirovaniya”, [Elektronnyi resurs]. Metod dostupa http://elis.dvo.ru