Convergence of the gradient projection method and Newton's method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 10, pp. 1733-1749
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The gradient projection method and Newton's method are generalized to the case of nonconvex constraint sets representing the set-theoretic intersection of a spherical surface with a convex closed set. Necessary extremum conditions are examined, and the convergence of the methods is analyzed.
@article{ZVMMF_2016_56_10_a4,
author = {Yu. A. Chernyaev},
title = {Convergence of the gradient projection method and {Newton's} method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1733--1749},
publisher = {mathdoc},
volume = {56},
number = {10},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_10_a4/}
}
TY - JOUR AU - Yu. A. Chernyaev TI - Convergence of the gradient projection method and Newton's method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2016 SP - 1733 EP - 1749 VL - 56 IS - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_10_a4/ LA - ru ID - ZVMMF_2016_56_10_a4 ER -
%0 Journal Article %A Yu. A. Chernyaev %T Convergence of the gradient projection method and Newton's method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2016 %P 1733-1749 %V 56 %N 10 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_10_a4/ %G ru %F ZVMMF_2016_56_10_a4
Yu. A. Chernyaev. Convergence of the gradient projection method and Newton's method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 10, pp. 1733-1749. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_10_a4/