A parametric method of linearization in mathematical programming problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 1, pp. 61-72
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The mathematical programming problem with constraints in the form of convex inequalities, and a method of linearization for solving the problem, are studied. It is shown that the method has all the properties of the classical gradient descent method, widely used in unconstrained optimization problems. The method does not employ evaluations of the second derivatives or their approximation, and converges with an arbitrarily chosen initial approximation.
@article{ZVMMF_1983_23_1_a6,
author = {V. M. Panin and B. N. Pshenichnyi},
title = {A parametric method of linearization in mathematical programming problems},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {61--72},
year = {1983},
volume = {23},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_1_a6/}
}
TY - JOUR AU - V. M. Panin AU - B. N. Pshenichnyi TI - A parametric method of linearization in mathematical programming problems JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 1983 SP - 61 EP - 72 VL - 23 IS - 1 UR - http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_1_a6/ LA - ru ID - ZVMMF_1983_23_1_a6 ER -
%0 Journal Article %A V. M. Panin %A B. N. Pshenichnyi %T A parametric method of linearization in mathematical programming problems %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 1983 %P 61-72 %V 23 %N 1 %U http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_1_a6/ %G ru %F ZVMMF_1983_23_1_a6
V. M. Panin; B. N. Pshenichnyi. A parametric method of linearization in mathematical programming problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 1, pp. 61-72. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_1_a6/