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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 4, Pages 602–625
(Mi zvmmf300)
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This article is cited in 48 scientific papers (total in 48 papers)
Duality-based regularization in a linear convex mathematical programming problem
M. I. Sumin Nizhni Novgorod State University, pr. Gagarina. 23, Nizhni Novgorod, 603950, Russia
Abstract:
For a linear convex mathematical programming (MP) problem with equality and inequality constraints in a Hilbert space, a dual-type algorithm is constructed that is stable with respect to input data errors. In the algorithm, the dual of the original optimization problem is solved directly on the basis of Tikhonov regularization. It is shown that the necessary optimality conditions in the original MP problem are derived in a natural manner by using dual regularization in conjunction with the constructive generation of a minimizing sequence. An iterative regularization of the dual algorithm is considered. A stopping rule for the iteration process is presented in the case of a finite fixed error in the input data.
Key words:
mathematical programming, linear convex problem, duality, regularizing alforithm, dual iterative regularization, stopping rule.
Received: 08.11.2006
Citation:
M. I. Sumin, “Duality-based regularization in a linear convex mathematical programming problem”, Zh. Vychisl. Mat. Mat. Fiz., 47:4 (2007), 602–625; Comput. Math. Math. Phys., 47:4 (2007), 579–600
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https://www.mathnet.ru/eng/zvmmf300 https://www.mathnet.ru/eng/zvmmf/v47/i4/p602
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Abstract page: | 1498 | Full-text PDF : | 234 | References: | 73 | First page: | 1 |
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