On the regularization of the Lagrange principle and on the construction of the generalized minimizing sequences in convex constrained optimization problems
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 3, pp. 410-428
Voir la notice de l'article provenant de la source Math-Net.Ru
We consider the regularization of the Lagrange principle (LP) in the convex constrained optimization problem with operator constraint-equality in a Hilbert space and with a finite number of functional inequality-constraints. The objective functional of the problem is not, generally speaking, strongly convex. The set of admissible elements of the problem is also embedded into a Hilbert space and is not assumed to be bounded. Obtaining a regularized LP is based on the dual regularization method and involves the use of two regularization parameters and two corresponding matching conditions at the same time. One of the regularization parameters is «responsible» for the regularization of the dual problem, while the other is contained in a strongly convex regularizing addition to the objective functional of the original problem. The main purpose of the regularized LP is the stable generation of generalized minimizing sequences that approximate the exact solution of the problem by function and by constraint, for the purpose of its practical stable solving.
Keywords:
constrained optimization, instability, dual regularization, regularized Lagrange principle, generalized minimizing sequence.
@article{VUU_2020_30_3_a4,
author = {M. I. Sumin},
title = {On the regularization of the {Lagrange} principle and on the construction of the generalized minimizing sequences in convex constrained optimization problems},
journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
pages = {410--428},
publisher = {mathdoc},
volume = {30},
number = {3},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VUU_2020_30_3_a4/}
}
TY - JOUR AU - M. I. Sumin TI - On the regularization of the Lagrange principle and on the construction of the generalized minimizing sequences in convex constrained optimization problems JO - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki PY - 2020 SP - 410 EP - 428 VL - 30 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VUU_2020_30_3_a4/ LA - ru ID - VUU_2020_30_3_a4 ER -
%0 Journal Article %A M. I. Sumin %T On the regularization of the Lagrange principle and on the construction of the generalized minimizing sequences in convex constrained optimization problems %J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki %D 2020 %P 410-428 %V 30 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/VUU_2020_30_3_a4/ %G ru %F VUU_2020_30_3_a4
M. I. Sumin. On the regularization of the Lagrange principle and on the construction of the generalized minimizing sequences in convex constrained optimization problems. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 30 (2020) no. 3, pp. 410-428. http://geodesic.mathdoc.fr/item/VUU_2020_30_3_a4/