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Home » Issues » Archive of Issues » 2020 - 3 issue » pp. 410-428

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Russia Nizhni Novgorod; Tambov
Year
2020
Volume
30
Issue
3
Pages
410-428
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Section Mathematics
Title On the regularization of the Lagrange principle and on the construction of the generalized minimizing sequences in convex constrained optimization problems
Author(-s) Sumin M.I.ab
Affiliations Nizhni Novgorod State Universitya, Tambov State Universityb
Abstract 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
UDC 519.853, 517.98
MSC 90C25, 90C46, 47A52, 65F22
DOI 10.35634/vm200305
Received 1 June 2020
Language Russian
Citation Sumin M.I. 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. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 3, pp. 410-428.
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