Two methods for minimizing convex functions in a class of nonconvex sets
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 10, pp. 1802-1811
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The conditional gradient method and the steepest descent method, which are conventionally used for solving convex programming problems, are extended to the case where the feasible set is the set-theoretic difference between a convex set and the union of several convex sets. Iterative algorithms are proposed, and their convergence is examined.
@article{ZVMMF_2008_48_10_a3,
author = {Yu. A. Chernyaev},
title = {Two methods for minimizing convex functions in a~class of nonconvex sets},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1802--1811},
year = {2008},
volume = {48},
number = {10},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_10_a3/}
}
TY - JOUR AU - Yu. A. Chernyaev TI - Two methods for minimizing convex functions in a class of nonconvex sets JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2008 SP - 1802 EP - 1811 VL - 48 IS - 10 UR - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_10_a3/ LA - ru ID - ZVMMF_2008_48_10_a3 ER -
Yu. A. Chernyaev. Two methods for minimizing convex functions in a class of nonconvex sets. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 10, pp. 1802-1811. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_10_a3/
[1] Demyanov V. F., Vasilev L. V., Nedifferentsiruemaya optimizatsiya, Nauka, M., 1981 | MR
[2] Chernyaev Yu. A., “Obobschenie metoda uslovnogo gradienta na odin klass nevypuklykh ekstremalnykh zadach”, Zh. vychisl. matem. i matem. fiz., 46:4 (2006), 576–582 | MR | Zbl
[3] Vasilev F. P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1980 | MR
[4] Loran P. Zh., Approksimatsiya i optimizatsiya, Mir, M., 1975