Geodesic
Iterative algorithm for minimizing a convex function at the intersection of a spherical surface and a convex compact set
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 10, pp. 1631-1640 
Yu. A. Chernyaev. Iterative algorithm for minimizing a convex function at the intersection of a spherical surface and a convex compact set. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 10, pp. 1631-1640. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_10_a3/
@article{ZVMMF_2017_57_10_a3,
     author = {Yu. A. Chernyaev},
     title = {Iterative algorithm for minimizing a convex function at the intersection of a spherical surface and a convex compact set},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1631--1640},
     year = {2017},
     volume = {57},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_10_a3/}
}
TY  - JOUR
AU  - Yu. A. Chernyaev
TI  - Iterative algorithm for minimizing a convex function at the intersection of a spherical surface and a convex compact set
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2017
SP  - 1631
EP  - 1640
VL  - 57
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_10_a3/
LA  - ru
ID  - ZVMMF_2017_57_10_a3
ER  - 
%0 Journal Article
%A Yu. A. Chernyaev
%T Iterative algorithm for minimizing a convex function at the intersection of a spherical surface and a convex compact set
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2017
%P 1631-1640
%V 57
%N 10
%U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_10_a3/
%G ru
%F ZVMMF_2017_57_10_a3

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

A numerical algorithm for minimizing a convex function on the set-theoretic intersection of a spherical surface and a convex compact set is proposed. The idea behind the algorithm is to reduce the original minimization problem to a sequence of convex programming problems. Necessary extremum conditions are examined, and the convergence of the algorithm is analyzed.

[1] Minnibaev T. F., Chernyaev Yu. A., “Iteratsionnyi algoritm resheniya zadachi matematicheskogo programmirovaniya s predvypuklymi ogranicheniyami”, Zh. vychisl. matem. i matem. fiz., 50:5 (2010), 832–835

[2] Chernyaev Yu. A., “Chislennyi algoritm resheniya zadachi matematicheskogo programmirovaniya s ogranicheniem v vide gladkoi poverkhnosti”, Zh. vychisl. matem. i matem. fiz., 56:3 (2016), 387–393 | DOI

[3] Chernyaev Yu. A., “Dva metoda minimizatsii vypuklykh funktsii na klasse nevypuklykh mnozhestv”, Zh. vychisl. matem. i matem. fiz., 48:10 (2008), 1802–1811

[4] Chernyaev Yu. A., “Iteratsionnyi metod minimizatsii vypukloi negladkoi funktsii na vypukloi gladkoi poverkhnosti”, Zh. vychisl. matem. i matem. fiz., 49:4 (2009), 611–615

[5] Golshtein E. G., Tretyakov N. V., Modifitsirovannye funktsii Lagranzha: Teoriya i metody optimizatsii, Nauka, M., 1989

[6] Golikov A. I., Zhadan V. G., “Iterativnye metody resheniya zadach nelineinogo programmirovaniya s ispolzovaniem modifitsirovannykh funktsii Lagranzha”, Zh. vychisl. matem. i matem. fiz., 20:4 (1980), 874–888

[7] Zhadan V. G., “Modifitsirovannye funktsii Lagranzha v nelineinom programmirovanii”, Zh. vychisl. matem. i matem. fiz., 22:2 (1982), 296–308

[8] Pshenichnyi B. N., Danilin Yu. M., Chislennye metody v ekstremalnykh zadachakh, Nauka, M., 1975

[9] Golikov A. I., Zhadan V. G., “Dve modifikatsii metoda linearizatsii v nelineinom programmirovanii”, Zh. vychisl. matem. i matem. fiz., 23:2 (1983), 314–325

[10] Antipin A. S., Nedich A., Yachimovich M., “Trekhshagovyi metod linearizatsii dlya zadach minimizatsii”, Izvestiya vuzov. Matematika, 1994, no. 12, 3–7

[11] Antipin A. S., Nedich A., Yachimovich M., “Dvukhshagovyi metod linearizatsii dlya zadach minimizatsii”, Zh. vychisl. matem. i matem. fiz., 36:4 (1996), 18–25

[12] Chernyaev Yu. A., “Skhodimost metoda proektsii gradienta dlya odnogo klassa nevypuklykh zadach matematicheskogo programmirovaniya”, Izv. vuzov. Matematika, 2005, no. 12, 76–79

[13] Chernyaev Yu. A., “Obobschenie metoda uslovnogo gradienta na odin klass nevypuklykh ekstremalnykh zadach”, Zh. vychisl. matem. i matem. fiz., 46:4 (2006), 576–582

[14] Chernyaev Yu. A., “Obobschenie metoda Nyutona na klass nevypuklykh zadach matematicheskogo programmirovaniya”, Izv. vuzov. Matematika, 2008, no. 1, 78–82

[15] Chernyaev Yu. A., “Obobschenie metoda proektsii gradienta i metoda Nyutona na ekstremalnye zadachi s ogranicheniem v vide gladkoi poverkhnosti”, Zh. vychisl. matem. i matem. fiz., 55:9 (2015), 1493–1502 | DOI

[16] Vasilev F. P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1980

[17] Dulliev A. M., Zabotin V. I., “Iteratsionnyi algoritm proektirovaniya tochki na nevypukloe mnogoobrazie v lineinom normirovannom prostranstve”, Zh. vychisl. matem. i matem. fiz., 44:5 (2004), 827–830

[18] Zabotin V. I., Arutyunova N. K., “Dva algoritma otyskaniya proektsii tochki na nevypukloe mnozhestvo v normirovannom prostranstve”, Zh. vychisl. matem. i matem. fiz., 53:3 (2013), 344–349 | DOI

[19] Arutyunova N. K., Dulliev A. M., Zabotin V. I., “Algoritmy proektirovaniya tochki na poverkhnost urovnya nepreryvnoi na kompakte funktsii”, Zh. vychisl. matem. i matem. fiz., 54:9 (2014), 1448–1454 | DOI

[20] Loran P. Zh., Approksimatsiya i optimizatsiya, Mir, M., 1975

[21] Demyanov V. F., Vasilev L. V., Nedifferentsiruemaya optimizatsiya, Nauka, M., 1981