Geodesic
Dual multiplicative algorithms for an entropy-linear programming problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 3, pp. 453-464 Cet article a éte moissonné depuis la source Math-Net.Ru

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A multiplicative-barrier generalization of the Cauchy gradient descent method is proposed and studied. The technique is used to search for dual variables in the entropy maximization problem with affine constraints, which arises, for example, in the simulation of equilibria in macroscopic systems. For this class of problems, the dual variables can be used to effectively determine the primal ones. The global convergence of the iterative algorithms proposed is proved. 
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E. V. Gasnikova. Dual multiplicative algorithms for an entropy-linear programming problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 3, pp. 453-464. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_3_a5/

[1] Fang S.-C., Rajasekera J. R., Tsao H.-S. J., Entropy optimization and mathemat. programming, Kluwer's Internat. Ser., 1997 | MR

[2] Popkov Yu. S., Teoriya makrosistem: ravnovesnye modeli, URSS, M., 1999 | MR

[3] Magaril-Ilyaev G. G., Tikhomirov V. M., Vypuklyi analiz i ego prilozheniya, URSS, M., 2003

[4] Polyak B. T., Vvedenie v optimizatsiyu, Nauka, M., 1983 | MR

[5] Evtushenko Yu. G., Metody resheniya ekstremalnykh zadach i ikh primenenie v sistemakh optimizatsii, Nauka, M., 1982 | MR | Zbl

[6] Aliev A. C., Dubov Yu. A., Izmailov R. N., Popkov Yu. S., “Skhodimost multiplikativnogo algoritma resheniya zadach vypuklogo programmirovaniya”, Tr. VNIISI. Dinamika ravnovesnykh sistem, Nauka, M., 1985, 59–67

[7] Belenkii V. Z., Volkonskii V. A. i dr., Iteratsionnye metody v teorii igr i programmirovanii, Nauka, M., 1974

[8] Zubov V. I., Ustoichivost dvizheniya, Vyssh. shkola, M., 1973 | MR | Zbl

[9] Opoitsev V. I., “Obraschenie printsipa szhimayuschikh otobrazhenii”, Uspekhi matem. nauk, 31:4 (1976), 169–198 | MR

[10] Zhadan V. G., Chislennye metody lineinogo i nelineinogo programmirovaniya: vspomogatelnye funktsii v uslovnoi optimizatsii, VTs RAN, M., 2002 | MR

[11] Dubov Yu. A., Imelbaev Sh. S., Popkov Yu. S., “Multiplikativnye skhemy iteratsionnykh algoritmov optimizatsii”, Dokl. AN SSSR, 272:6 (1983), 1304–1306 | MR | Zbl

[12] Dubov Yu. A., Imelbaev Sh. S., Popkov Yu. S., “Multiplikativnye algoritmy v ekstremalnykh zadachakh”, Tekhn. kibernetika, 1984, no. 1, 30–36 | MR | Zbl