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# A version of the penalty method with approximation of the epigraphs of auxiliary functions

 dc.contributor.author Zabotin I. dc.contributor.author Kazaeva K. dc.date.accessioned 2020-01-15T22:14:55Z dc.date.available 2020-01-15T22:14:55Z dc.date.issued 2019 dc.identifier.issn 2541-7746 dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/157223 dc.description.abstract © 2019, Kazan Federal University. All rights reserved. A method for solving the convex programming problem, which is ideologically close to the known methods of external penalties, was proposed. The method uses auxiliary functions that are built on the general form of the penalty functions. In order to find approximations, the epigraphs of these auxiliary functions, as well as the original problem’s domain of constraints, were immersed in certain polyhedral sets. In this regard, the problems of finding the iterative points are the linear programming problems, in which the constraints are the sets that approximate the epigraphs and a polyhedron containing an admissible set. The approximating sets were constructed using the traditional cutting of iterative points by planes. The peculiarity of the method is that it enables a periodic update of the approximating sets by discarding the cutting planes. The convergence of the proposed method was proved. Its implementation was discussed. dc.relation.ispartofseries Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki dc.subject Approximating set dc.subject Conditional minimization dc.subject Convergence dc.subject Cutting hyperplane dc.subject Epigraph dc.subject Iterative point dc.subject Penalty function dc.title A version of the penalty method with approximation of the epigraphs of auxiliary functions dc.type Article dc.relation.ispartofseries-issue 2 dc.relation.ispartofseries-volume 161 dc.collection Публикации сотрудников КФУ dc.relation.startpage 263 dc.source.id SCOPUS25417746-2019-161-2-SID85075210659
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• Публикации сотрудников КФУ Scopus [24551]
Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.